Vol.14/No.53/Nov2017
Received 2017/02/06
Accepted 2017/08/23
Persian translation of this paper entitled:
)گونهشناسی بافت نمای شهری (با رویکرد شکلی
)(نمونه موردی میدان امام خمینی(ره) تهران
is also published in this issue of journal.
The Typology of Urban Façade Texture (in an approach to shape scrutiny)
(Case study of Imam Khomeini Square in Tehran)
Seyed Ali Seyedian*
Saeed Alinia**
Vahid Heidar Nattaj***
Abstract
In studying the architectural evolutions, it is necessary to scrutinize the climatic, shape and historic
typologies. Reviewing these studies clariies the researchers’ view in using the typology as a type
methodology in designing different architectural properties such as the plan, mass, form, and space. For
instance, Olgy reviewed and categorized architecture in terms of architectural formation due to climatic
features and Durand and Krier focused on the geometric aspects of the plans. Therefore, this paper tries
to offer a typology of facades as a signiicant aspect of architectural design since the absence of deining
a proper process in façade design has led to the development of an unpleasant cityscape and inconsistent
individualistic façade design all over the city.
Therefore, this paper queries the geometric and typological features in the facades of valuable buildings
(traditional buildings) during different periods. In this regard, this research is conducted assuming that
the correct identiication and recognition of façade typology and its re-establishment in the contemporary
works can hinder insipidity and chaos in cityscape while preserving the historical-cultural authenticity
of the facades. Thereafter, the research is continued by drawing the basic shapes (square, triangle, and
circle) according to Durand’s and Krier’s - by whom these shapes were introduced as the basic shapes in
the typology of shapes – viewpoints as well as applying changes to the axes, vertices, and sides of these
shapes in the opinion of Durand’s and Krier’s transformation principles in shapes in order to ind the
transformation trajectory in these shapes. Hence, the building facades around Imam Khomeini Square which is a signiicant urban, social, political, cultural, and historical place- in Tehran city are scrutinized
by library research (books and articles) and in analytical –comparative research method by studying the
facades (pictures and illustrations) using 9 statistical populations from Qajar, Pahlavi I, Pahlavi II and the
contemporary era (two slides from each of the four sides of the square on average). Eventually, it was
concluded that the most of the geometric patterns used in the facades of the surrounding monuments during
Qajar period were formed by combination or application of simple shapes such as circles and squares based
on the center of the circle or in the process of repetition in terms of geometry, ornaments, and apertures.
These terms during Pahlavi I period have appeared in form of triangular shapes and acute sections in
a variety of combinations with a circle and a square. As for the Pahlavi II period, the inluence of the
principles of Western architecture led into the use of simplicity and maximum prevention in decorations
in various constructions of different functions. As a result, the geometric patterns used in this period were
mostly squares and the products from the square rotation in angles.
Keywords
Historical typology of the facade, basic shapes in façade, evolution of shape in facades, urban facade, Imam
Khomeini Square in Tehran.
*. Assistant Professor in architecture, faculty of arts and architecture, University of Mazandaran. Corresponding author, a_seyedian@umz.ac.ir
**. M.A. student in architecture, faculty of arts and architecture, University of Mazandaran. saeed.alinia@ymail.com
***. Assistant professor, faculty of arts and architecture, University of Mazandaran.v.heidarnattaj@umz.ac.ir
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Introduction
During the eighteenth and nineteenth centuries,
lourishment of various sciences in Western Europe,
especially in France and England, led to great advances
(Bernal, 2001: 385). At that time, Durand, who was
practicing the theoretical foundations of architectural
science, and other scientists such as Laplace1 and
Monge2 were the most prominent professors at the
Polytechnic University of Paris (Madrazo, 1194:
14). since the theoretical debates in architecture were
most affected by the science of biology, two theories
of the independent formation of species (Fixism)
and the gradual evolution of the traits of species
(Transformisme) in science inluenced architecture
and the study of architectural history in particular
(Sahabi, 1996:4). Focusing on the relationship
between theories and the historical origins of the
beings, Durand offered a form of typology to classify
various buildings according to their plan and drawings
(Wojtowicz, Jery: 1986). Therefore, he introduced
the basic shapes (square, rectangle, and circle) and
their combinations. In his drawings, he deined the
major and minor axes of these shapes and described
the sides as the axes and completed it by drawing of
the rest of the elements including the columns and
windows (Memarian, 2012). Subsequently, Krier
who was considered a neo-modernist emphasized
on the return to the architectural history and studied
and criticized architectural works in three scales of
urban, architectural and interior design (Krier, 1984).
He researched on the origins of these features in the
urban scale by comparing urban and architectural
elements; square and street and rooms and corridors.
He presented these studies as the common elements
of architecture and urbanism in two different scales
(Memarian, 2012). In the irst in researching the
process fo shape, he introduced the basic elements as
the square, triangle and circle, and scrutinized them by
the six principles of transformation in three aspects of
function, structure, and form (Ibid). It is believed that
identifying the trajectory of these changes and patterns
from the past to the present, as well as deining a
fundamental and logical approach in facade design can
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16
lead to understanding of the origins of transformation
and avoid the chaos caused by individualism in façade
design.
Therefore, this paper studies the evolution of the
typology of urban facade texture in Imam Khomeini
Square (Toopkhaneh Square) in Tehran in the four
main direction. Here, the telegraph and telephone
building (current telecommunications building) on
the south side of the square, Baldieh building (former
municipality) on the north side of the square, Shahi
Bank (Current Tejarat Bank) on the east side of
the square and the trafic ofice (current the Imam
Khomeini metro station) on the west of the square are
studied as valuable in formation of this urban space
in the following headings: 1. Research background
2. Description and recognition of shape approach 3.
Identiication of the basic shapes in architecture 4.
Categorization of shape transformation in the basic
shapes (as claimed by Krier) 5. Transformation of the
basic shapes (as claimed by Durand) 6. Categorization
of the building facades surrounding Toopkhaneh
Square according to their location and construction
time 7. Adaptation of the derived patterns to the
categorized facades 8. The evolution process of
geometric patterns 9. Achieving the geometric
transformation pattern in façade design.
Research background
Studying of type and typology are among global
subjects which are addressed by architects and other
scholars in the historical script since two thousand
years ago and it has been known for over 250 years
speciically in the ield of science. In his the then
books on architecture, Vitruvius has categorized
various types of Greek buildings, including houses,
temples and public buildings (about 2000 years ago).
For instance, residential buildings are categorized into
houses with courtyards and house without courtyards.
As for the temples, they are classiied into various types
based on the number of outer pillars and the quadruple
classical systems. Following that, the scientiic
categorization of the Swedish Carl Linné in botanical
sciences led other scientists to take action and pursue
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
this trend in architecture from the late eighteenth
century (Memarian and Tabarsa, 2013). De Quincy
(De Quincy, 1844), who published The Historical
Dictionary of Architecture in 1844 discusses the type
and model. He describes type as a sketch or a scheme
that is able to inluence the artist’s mind, while a model
is an imitable object or idea (De Quincy, 1844). Also,
many other researchers, such as Aldo Rossi, Argan
and Iimonito, have discussed this subject as well. In
the 1990s, the subject of typology was discussed at the
Harvard, MIT and Birmingham universities and the
use of typology in architectural knowledge continued
seriously up to the early twentieth century. Sidney
Addy used the typography in his book The Evolution
of the English House and Matthews used it in his book
of English house. In this regard, the idea of classifying
buildings based on common features started in Iran for
about three decades, among which one can refer to the
typology of housing in Kandovan village (Homayoun,
2007).
The type is also a key concept in architecture and
urbanization and has been studied by many authors
(Rapaport, 1990; Moudon,1994; Radberg,1996).
A type as a concept refers to a form, a class or
a group of people or a collection of objects that
are common in distinct characteristics that
distinguish them among other people or groups of
objects (Rapaport, 1990: 48). In fact, according
to Rappaport, “typology is an attempt to put a set
of complex objects into a systematic collection I
order to achieve more generality in recognition and
planning” (Zakerhaghighi, Majedi & Habib, 2010).
Description and recognition of shape
approach
...........................................................
According to the art history, a work of art is divided
into forms, igures, shapes, and contents (Memarian,
2012: 57). The important point in the process of
applying the shape in architecture is relating it to other
elements, structures or functions. Since the eighteenth
century, graphic geometry was used to transform
geometry into the reality and analyze it in different
building facades. This approach made architecture as
a process of combining or processing shapes. Durand
(1795) who coincided with Buffon’s historicalevolutionary theory in his teaching of architecture,
beneitted from the theory of gradual change. He
introduced it in the classiication of plans and roofs
of buildings from simple to complex; because unlike
technical sciences, the product of shape is derived from
a general process and a shape is a tool for realization
in art studies especially architecture.
Durand focused on the history of architecture by
referring to the style and disregarding of building
location and time period, so that time and location
borders were ignored in his shape analysis and
understanding. For instance, he simpliied the complex
Saint Peter Cathedral into rectangular (Basilica) and
circular (the square) shapes in one of his drawings and
presented his proposed design as a combination of a
rectangular square and a simple basilica-shaped space
(Durand, 1800). In the light of this, Krier interpreted
the space types such as the square, the street, and
building plans into simple shapes. He then achieved
24 states of shape by applying his six principles
of transformation (i.e. transformation, overlying,
integration, addition, sector and changing the angle)
in both conditions of (ordered and disordered) and
(opened and closed). This approach was considered
a technique in recognition of geometric patterns
designed in building façade, mass, and form. It follows
a referable and accepted geometric procedure in the
science of geometry and leads to a full understanding
of elements used in the building façade. Recognition
of these elements helps us understand the formation
and transformation of shapes. In this study, by
applying the Krier’s six principles on basic shapes
and regarding their geometric features (vertices,
sides, diameters, and center), the quadruple process
of breaking, repetition, angle and combination were
achieved. These processes have been analyzed as
transformation principles in shape and they are studied
in the facade of Imam Khomeini Square.
Identiication of the basic shapes in architecture
The architecture science is continuously derived
from a geometric process in which the design lines
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are organized in a mental process by the designer.
Therefore, application of geometric patterns is very
signiicant in designing the plan as the building
outlay, in the façade as the building appearance,
and in the mass as the building form. Therefore,
identifying the basic shapes and the way in which
they are geometrically combined does not go far
beyond the expectation of recognizing the past used
patterns. In this regard, the foundations of the works
of Durand and Krier was codiied on the basis of
building classiication according to their outlay.
Durand believed in simplifying the existing realities
to geometric shapes and categorizing them in different
groups (Memarian, 2012: 55). In categorizing the
elements, composite components, and inal products,
Durand used the shapes that were common in features
and in having basic shapes such as squares, rectangles,
and circles. In this way, he derived new combinations
based on common geometric properties such as the
axis of symmetry. Krier also took the irst action
in identifying the shape formation process was by
simplifying spatial types such as square, street, and
building plans into basic shapes (Memarian, 2012: 73).
In other words, the forms were simpliied according to
Gestalt in order to better understand the environment.
............................................................
Categorization of shape transformation in the
basic shapes
The transformations of basic shapes as the geometry
of the building was described to the inseparable
connection of function, structure and form by Krier
after the motto of modern architects that asserted
“forms follows function”. He presented the changes
of basic shapes and the process of transforming the
basic elements into spatial forms and shapes in six
categories (the change of the angle, sector, addition,
merging, overlaying, and transformation), regardless
of the geometric features of the basic shapes.On the
other hand, Durand believed that the shapes can be
combined based on their major and minor axes from
simple to complex. He also believed that the shapes
can be combined by repetition of their axes in different
directions, repeatition of square shapes or their mirror
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18
relecting (Wojtowicz. Jery, 1986). Since Krier
believed transformation occur by changing a member
of a basic shape, such as angular illet or delection, it
seems less convincing as compared to Durand’s work,
in which the shapes were repeated or integrated on
the basis of one or two geometric axes and expanded
from simple to complicated (Memarian, 2012: 75).
Therefore, the possible and acceptable geometric
transformations that are formed by using the geometric
axis of the basic shapes will be discussed in this study.
Research method and the statistical
population
In order to investigate the shapes of the buildings
surrounding Imam Khomeini Square (Toopkhaneh
Square) in Tehran, a three-stage process was carried
out: 1. Identiication of the basic shapes, their
transformations, and their geometric derivatives. 2.
Identiication of transformations in Imam Khomeini
Square (Toopkhane Square) in Tehran in the four
main directions from Qajar to the contemporary era.
3- Adaptation of geometric patterns to the achieved
facades and identifying the geometric transformation
process. This research is conducted by library research
(books and articles) and in analytical –comparative
research method by studying the facades (pictures
and illustrations) using 9 statistical populations from
Qajar, Pahlavi I, Pahlavi II and the contemporary era
(two slides from each of the four sides of the square
on average). The data are categorized based on the
construction time and location of the facades in order
to better understand and percept the square space from
Qajar period to the contemporary era.
Transformation of the basic shapes
Transformation of the basic shapes by Krier’s
categorization can be studied via reviewing the basic
shapes and their combination according to the main
axes, sides, and vertices. The applied transformations
are classiied into four general categories: delection,
the change of the angle, repetition, and composition.
The purpose of this categorization is to achieve a
holistic geometric framework that can encircle all
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
possible geometric transformations of the basic shapes
for further identiication of forms and geometric
combinations in plan, facade, mass, and form of the
constructions.
Delection process
This process occurs separately, dependent on the
geometric characteristics of every basic shape. In
rectangles, the delection process is performed on the
diameters, axes or it is performed by the combination
of both actions. In triangles, this process is carried out
according to the center and in circles, the delection
process is performed based on diameters, radii, and
chords.
Angle Process
In this process, the angles of the basic shapes are
changed and the resulting sections are considered
as the derivative of the basic shapes, which can be
used in the general form of facades, ornaments, and
geometry of apertures. The shapes derived from
changing the angles of a square are the rhombus, the
parallelogram, the right trapezoid, the trapezoid, and
the rectangle. The shapes derived from changing the
angles of the equilateral are the right triangle l (1.
isometric 2.axonometric) and equilateral triangle. The
derived shape from changing the angle of the circle is
the ellipse (Fig. 1).
Combination process
Repetition process
This process is carried out by multiplying a section
without combining it with other sections. In this
process, rectangular and triangular shapes are repeated
on the center, vertices, and sides, and circular shapes
are repeated around the center and the chords. A
combination of the obtained sections can be observed
in the façade ornaments.
In contrast to the three previous processes in which
the sections were separately involved in the process,
in this process the sections are combined two-by-two
according to their four common geometric factors: the
center, the vertices, the sides, and the axis. Here, the
combination process is divided into the basic sections,
the derivatives, and the extensions. In the column of the
basic sections, the basic shapes are mentioned based
on the geometric factors. In the column of derivatives,
...........................................................
Fig. 1. Geometric transformation (delection, repetition and change of the angle) in the basic shapes. Source: authors.
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the possible geometric combinations are mentioned
in two rows of the primary and secondary derivatives
(the row of secondary derivatives is in fact obtained
from the combinations of primary derivatives. when
possible, further sections are inserted into the column
section expansion (Fig. 2, 3, 4).
This stage of the research was aimed at achieving the
complex shapes by using the basic shapes and their
geometric properties. In the following, the products
of these combinations are identiied and reread in
the signiicant elements of the facades such as the
overall façade frame, apertures, and ornaments. These
obtained sections are used as a geometric reference
for the geometric patterns s used in the facade, the
general form, the geometry of the apertures, and even
the ornaments. Finally, the geometric principles in
façade design were adapted to the achieved geometric
patterns in order to perceive the geometric evolution
during the mentioned periods.
............................................................
Categorization of the building facades
surrounding Toopkhaneh Square according
to their location and construction time
Mashgh Square (Imam Khomeini Square) in Tehran
was built in 1867 during Nasereddin Shah Qajar’s
reign, by an order of Mirza Taghi Khan Amir Kabir in
about ten years. After its formation, the surrounding
uniform regular buildings around this place were
destroyed and Shahi bank was constructed on the
east side of the square. Thereafter, Baladieh building
(which literally means municipality) was built on the
north side of the square, and eventually the Wireless
communication ofice was added on the south side
of the square which was neighbored with the Police
ofice after a while. Finally, the trafic ofice was
built on the southwest side and the new Bank of
Commerce was constructed following the destroying
of Shahi Bank. Subsequent to these proceedings, the
Wireless communication ofice was replaced by the
post, telegraph and telephone ofice. This square is
one of the irst places in Tehran which was irst stone
paved - and later surfaced with asphalt. Toopkhaneh
Square has long been the center of trafic in Tehran,
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20
as well as a place for gathering storms of protests.
During the constitutional period, this square was
illed with crowds of protesters due to being close to
the Arg-e Saltanati (the royal citadel) and Baharestan
Square (http2).
Having identiied and collected the data from the
facades in 9 statistical population (9 buildings),
the buildings were categorized based on their
time of construction and location for further
understanding of the square space from Qajar period
to the contemporary era. These 9 buildings include
Baldieh, Post and Telegraph, Telecommunication
building, Shahi Bank, Bank of Commerce (current
Tejarat Bank), Police ofice, Road Administration,
Museum of Industry and Imam Khomeini Metro
Station buildings. In the following table, the vertical
comparison of the facades leads to understanding
of the historical transformation of the square in
the mentioned period. In addition, the horizontal
comparison of buildings reveal the general common
shapes in the building form and elements used in
ornaments and apertures.
The evolution of the building facades surrounding
Mashgh Square in the four main directions (Fig. 5):
Adaptation of the derived patterns to the
categorized facades
In order to adapt the geometric patterns to the facades
of the categorized buildings (table above) according
to the four main directions, a simulation of the overall
forms, apertures, and ornaments was conducted on
the square sides (north, south, east, and west) during
the mentioned course of time. In the tables below,
the facades on every side were simulated according
to their location and construction time on the left
and according to their simulated geometry and their
transformations, geometric patterns of the basic
shapes and their derivatives on the right.
The geometric transformations created in the
basic shapes was clariied based on the quadruple
transformation principles of delection (sector),
repetition, composition, repetition, and angle by the
help of color according to the guidance given below
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Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
Fig. 2. Geometric transformation (combination of the circle and the
square) in the basic shapes. Source: authors.
Fig. 3. Geometric transformation (combination of the triangle
and the square) in the basic shapes. Source: authors.
...........................................................
Fig. 4. Geometric transformation (combination of the rectangle and the circle) in the basic
shapes. Source: authors.
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Baladieh building (Qajar
- 1866)
In this period, the overall form of the building, the apertures, and the ornaments are shaped of simple
sections from circles and squares, and the major used processes are the simple processes of combining
a circle and a square around the center of the circle and the deflection process on the axis.
Baladieh building (Qajar
- 1887)
In this period, Baladieh building was renovated and the hallway was extended to the building. Alike
the previous period, the overall form of the building, the apertures, and ornaments are formed of
simple sections of circles and squares; however, the simple process of combining the square and the
circlr (on the center of the circle) was accompanied by the process of the changing of the angle and
transformation of a circle to an ellipse.
Baladieh building
(Pahlavi I-1937)
In this period, acute and triangular sections are observed in the facade. A clock element was added to
the hallway and three processes are observed at this stage of time; combination of the circle and square
based on the square vertices, combination of the circle and square based on the vertex of the circle, as
well as the combination of the circle and triangle.
Baladieh building
(Pahlavi II-1951)
Having added an entrance in this period, the clock element above the hallway was transformed and the
building was completed using a combination of complex processes. The pattern used in the
construction of the clock element above the hallway was shaped by deflection process of the circle on
its diameter as well as the angle process
Baladieh building
(Pahlavi II-1956)
In this period, Baladieh building spends its last days of existence regarding a different change of the
hallway in comparison to the previous periods. At this stage, the hallway is thoroughly transformed
following the patterns of modern architecture and the angle transformation process of square to
rectangle.
............................................................
Fig. 5. The evolution of Imam Khomein Square (Tupkhaneh) in Tehran from Qajar period (construction time) to the contemporary era, categorized
according to the four main directions. Source: authors.
of each table. The yellow sections represent the
adapted pattern derived from the combination of two
or more processes. They are considered as an added
element and a distinguishing feature in the facade
compared to the previous period.
At this stage, the prevailing geometric patterns of
every period is introduced by recognition and rereading of ornaments and the overall forms of the
building facades as well as the adaptation of the basic
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22
shape patterns to façade elements. Having identiied
these patterns, the geometric aspects of façade design
and the signiicance of geometric transformation and
combination can be acknowledged in each period.
A)Adaptation of the north façade to the geometric
patterns (Fig. 6):
B)Adaptation of the south façade to geometric
patterns (Fig. 7):
C) Adaptation of the south façade to geometric
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
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patterns (Fig. 8):
D) Adaptation of the south façade to geometric
patterns (Fig. 9):
The evolution process of geometric patterns
Having identiied the basic shapes and their
transformations, a framework called the Pattern
of Geometric transformations was achieved in
this paper in which the geometric patterns and
appearance properties of facades (including the
total combination, apertures and ornaments) were
adapted and compared by historical-evolutionary
categorization. In addition, the trajectory of these
changes was searched by investigating the evolution
of the geometric patterns used in facades. Therefore,
in the table below, the facades located at the four
main directions around the square were presented
in form of a linear spectrum from Qajar period to
In this period, the overall form of the building, the apertures, and the ornaments are shaped of simple
sections from circles and squares, and the major used processes are the simple processes of combining
a circle and a square around the center of the circle and the deflection process on the axis.
Baladieh building (Qajar
- 1887)
In this period, Baladieh building was renovated and the hallway was extended to the building. Alike
the previous period, the overall form of the building, the apertures, and ornaments are formed of
simple sections of circles and squares; however, the simple process of combining the square and the
circlr (on the center of the circle) was accompanied by the process of the changing of the angle and
transformation of a circle to an ellipse.
Baladieh building
(Pahlavi I-1937)
In this period, acute and triangular sections are observed in the facade. A clock element was added to
the hallway and three processes are observed at this stage of time; combination of the circle and square
based on the square vertices, combination of the circle and square based on the vertex of the circle, as
well as the combination of the circle and triangle.
Baladieh building
(Pahlavi II-1951)
Having added an entrance in this period, the clock element above the hallway was transformed and the
building was completed using a combination of complex processes. The pattern used in the
construction of the clock element above the hallway was shaped by deflection process of the circle on
its diameter as well as the angle process
Baladieh building
(Pahlavi II-1956)
In this period, Baladieh building spends its last days of existence regarding a different change of the
hallway in comparison to the previous periods. At this stage, the hallway is thoroughly transformed
following the patterns of modern architecture and the angle transformation process of square to
rectangle.
Fig. 6. Adaptation and comparison of the north façade evolution to the geometric patterns. Source: authors.
...........................................................
Baladieh building (Qajar
- 1866)
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South façade (Qajar - 1866)
The general forms of the arches and vaults in the south facade are achieved by circle
and square combination on the center of the circle. Here, the circle is turned into an
ellipse in the process of angle transformation, by which the shape of the vaults is
formed.
South façade (Place of watching
cavalry and infantry marchingQajar-1979)
In this period, a new ornamental pattern is observed above the south façade which is
used as the place for watching military marching. In this pattern, the repetition of
circles around a central circle based on the center of the circle along with the process of
combination with square is perceived.
Post and Telegraph building
(Pahlavi I- 1936)
Telecommunication building
(Pahlavi II-1972)
In this period, with the advent of patterns that are composed of triangular cross
sections, triangular shapes appeared in the façade, apertures and the overall form of the
building such as the pediments above the entrance. The top dome form is created by
two processes: 1. The combination of a circle and a triangle on the center of the circle;
and 2. The combination of the triangle and the square based on the side of the square.
Following the advent of modern architectural principles, the overall form of the
building and apertures are shaped by the process of angle transformation form square
to rectangle.
Fig. 7. Adaptation and comparison of the south façade evolution to the geometric patterns. Source: authors.
............................................................
Shahi Bank (Qajar- 1898)
Bank of Commerce
(Pahlavi I-1931)
In this period, some elements can be recognized after destroying of the initial
construction and the construction of Shahi bank. The general form of the arches is
derived from the simple combination of circles and squares based on the center of the
circle. As for the ornaments, the pattern is created by repeatition of circles around a
circle on the center of the central circle in combination with square.
In this period, triangular sections and their combination with other sections were seen
in the facade and the overall form of the buildings. In this building, the hallway form is
created by the process of angle transformation by which square is turned into
rectangle. The shape products were combined with the sections of the square and
circle. Furthermore, the angle transformation process and changing of square to
rectangle is observed in the overall form of the building.
Fig . 8. Adaptation and comparison of the east façade evolution to the geometric patterns.
Source: authors.
..............................................................................
24
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
Police office and Traffic office
(Pahlavi I-1909)
Traffic office (Pahlavi II1931)
Imam Khomeini metro station
(contemporary-1999)
In this period, triangular cross sections are observed in different parts of the
building, including roof cover. The triangular patterns of Police office
building are not visible from the square, and the bulding's patterns are created
through traditional processes of combining circle and square and based on the
side of the square which are obvious in the forms of the arches.
In this period, the dominant process is angle transformation and change of
square to circle. In the structure of the road administration building, even the
general triangular shapes used in the façade are resulted from overlaying of
rectangular shapes in form of stairs (mastaba).
In this building, the ideas of traditional and modern patterns are both used in
the process of angle transformation and changing of circle into ellipse and
square into rectangle. Subsequently, the shapes used in the façade are created
by application of combiantion process.
Fig . 9. Adaptation and comparison of the west façade evolution to the geometric patterns. Source: authors.
Achieving the geometric transformation
pattern in façade design
The evolution of the overall form, apertures, and
ornaments in was achieved by arranging the building
façades according to their time of construction and
sorting and investigating their transformation. Since
the main objective of this research is to recognize
the prevailing geometric patterns in each period, the
facades and the patterns are categorized based on the
priority of recognition of the basic shapes and their
evolution.
The irst man-made houses were in circular shape,
according to the technical principles and in order
to solve the problem of ceiling spanning; hence,
some people believe that humans inspired the circle
from nature and its elements such as the sun and
the moon (Leitkouhi, 2011). Amon other examples
of primary circular buildings is the widely known
Arkim citadel. It is located in the south of Russia
(http2) near Kazakhstan (5000 B. C). Khosrowshahr
...........................................................
the contemporary era, and their shape transformation
was explained in every box correspondingly. It was
determined that during Qajar period (construction),
the use of simple combinations of basic shapes with
very slight changes in the overall form, apertures,
and ornaments in the four directions surrounding
the square are due to the simplicity of the design
in that period. By commencing of Pahlavi I era and
the arrival of modern style (Western architecture)
and its integration with traditional architecture, we
are dealing with complex patterns that are aimed at
bringing the traditional architecture closer to modern
architecture. During Pahlavi II era and following the
unconditional acceptance of modern architecture
principles (western architecture), the design are
tended toward simple shapes in the overall form and
apertures of the building (Fig. 10).
..............................................................................
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
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Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj/ Bagh- e Nazar, 14 (53):15-32
(Shah) building in Hamadan (5-4,000 BC) is another
example. Therefore, the circle can be considered as the
starting point for the geometric formation of shapes.
Another well-known building in circular shape is
the Stonehenge building in Salzburg in the south of
England (Zarei, 2006).
Subsequently, the circle shape was transformed and
turned it into irregular shapes by applying delections
and vertices which led to creation of irregular
shapes similar to the rectangle and the square. The
examples of these shapes are clearly evident in
dwellings such az Teppe Zaghe formed thousands
of years ago (about 4000 BC) with rectangular and
unconstrained square plans. In the next stage, the
attitude towards triangular patterns were observed in
some buildings such as the Egyptian Pyramids (2500
BC) wich were originally in the form of mastabas
Qajar period
North
side,
from
Qajar
period
to the
contem
porary
time
South
side,
from
Qajar
period
to the
contem
porary
time
............................................................
East
side,
from
Qajar
period
to the
contem
porary
time
West
side,
from
Qajar
period
to the
contem
porary
time
Baladieh building
(1866)
Baladieh building
(1889)
South side ( place of cavalry and infantry
marching-1889)
Shahi Bank (1898)
The uniform west façade before destruction
Pahlavi I period
Pahlavi II period
Late Pahlavi II
and the
contemporary
period
Baladieh building
(1937)
Baladieh building (1951)
Baladieh building (1956)
Post and Telegraph
building (1936)
Telecommunication building (1972)
Bank of Commerce (1931) – current Tejarat Bank
Police office and
Traffic office (1909)
Traffic office (1931)
Imam Khomeini metro
station (1999)
Fig. 10. The evolution of geometric patterns in the mentioned facades from Qajar period to the contemporary
era. Source: authors.
..............................................................................
26
(stepped frustum); (Zarei, 2006) (Fig. 13, 14).
Euclid also categorized the circles, squares, and
triangles as the basic shapes and introduces them as
Euclidean shapes (D.K.Ching, 2006). As a result, the
indings of the geometric patterns over time reveals that
the circles can be considered as mother of shapes from
which the squares and triangles are derived (Fig. 15).
In the following, the typology of the evolution of
the facades surrounding Imam Khomeini Square
(Toopkhane) in Tehran was achieved through
classiication of facades and their geometric patterns
regarding the prevailing geometric shape in every
era due to the technique of implementation, the
degree of Western architecture inluence and other
factors. Therefore, the dominant shape in every
period is recognized by categorization of changes
in basic shapes (and their hypernyms) as well as the
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
Fig. 11 & 12. Arkiam citadel in Russia and its circular shape. Source: http://senyawa-kimia.blogspot.com
Fig. 13. Teppe Zaghe. Source: Introduction to world architecture.
Source: author.
Fig. 14. The Egyptian pyramid.
Source: http://senyawa-kimia.blogspot.com
Fig. 15. The pattern of transformation in the basic shape. Source:
author.
Discussion (Analysis of the indings)
Considering the importance of façade design in terms
of visual signiicance in architecture, it is necessary
to establish a speciic method in designing the
building facade and ease the reading of the facades
of valuable monuments in order to preserve their
...........................................................
classiication of facades. Concerning the evolution
of geometric patterns, 5 milestones in façade design
were recognized. These milestones were identiied
as circles, squares, triangles, circles, and ultimately
squares, respectively (Fig. 16).
The above comparison and classiication reveals that
most of the geometric patterns used in the facades
of the surrounding monuments during Qajar period
were formed of simple shapes such as the circles and
squares or their combination according to the center
of the circle or in the process of repetition. During
Pahlavi I, the triangular shapes and sections with acute
angles were appeared in a variety of combinations
with circles and squares. As for the Pahlavi II period,
the inluence of Western architecture issued simplicity
and prevented ornaments in various constructions of
different functions. As a result, the geometric patterns
used in this period were mostly squares and the
products from square rotation in angles to the extent
that in the present day the use of curved and diagonal
lines, which are by some means derived from the
circle, are used only as a symbol of traditional and past
architecture (Fig. 17).
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The process of using basic shapes along the course the square evolution
North
side,
from
Qajar
period
to the
contem
porary
time
South
side,
from
Qajar
period
to the
contem
porary
time
............................................................
East
side,
from
Qajar
period
to the
contem
porary
time
West
side,
from
Qajar
period
to the
contem
porary
time
Baladieh building
(Pahlavi II-1956)
The deflection process
in a circle (sector)
according to the circle
diameter and
transformation to
semicircle geometric
pattern
The process of
changing the angle and
transformation of the
square to a rectangular
geometric pattern
Baladieh building
(Pahlavi I- 1937)
The process of
combining a square and
a circle
The process of
combining a square and
a circle (the circle is
transformed to an
ellipse under the
process of changing the
angle)
The process of
combining a square and
a circle based on the
center of the square
along with the process
of combining a square
and a circle around the
center of the circle and
merging it with the
process of combining a
triangle and a square
South side (Qajar)
South side ( the place
of cavalry and infantry
marching- Qajar-1879)
Post and Telegraph
office (Pahlavi I-1936)
Telecommunication building (Pahlavi II- 1972)
The process of
combining a square and
a circle (the circle is
transformed to an ellipse
under the angle
transformation)
The process of
combining the circle
and the square (under
repetition process
around the center of the
central circle)
The process of
combining a triangle and
a circle on the basis of
the center of the circle
as well as merging it to
the process of
combining a triangle and
square
The process of changing the angle and transforming
of the square to a rectangular geometric pattern
There is no
evidence of the
uniform east façade
Shahi Bank (Qajar1898)
____
The process of
combining a circle and
a square on the square
side as well as merging
it to repetition process
around the center of the
circle
Bank of Commerce (Pahlavi I- 1931)- current Tejarat Bank
The process of changing the angle and transformation of a square to a rectangle
followed by the simultaneous process of combining a triangle and a circle and
merging it to the process of changing the angle and transformation of a square to
geometric rectangular patterns
The uniform south façade before destruction (Qajar)
The process of combining a circle and a square (the
circle is transformed to an ellipse under the process
of changing the angle)
Police office and Traffic
office (Pahlavi I-1909)
Traffic office (Pahlavi
II-1931)
Imam Khomeini metro
station (contemporary1999)
The process of
combining a triangle and
square merged with the
process of combining a
square and a circle
The process of changing
the angle and
transforming of the
square base into a
rectangular geometric
pattern
The process of changing
the angle of a circle to a
ellipse merged with the
process of changing the
angle of a square to a
rectangle
Fig. 16. Categorization of geometric patterns and facades around the square based on the evolution of the basic shapes. Source: author.
..............................................................................
28
Baladieh building
(Pahlavi II-1951)
Baladieh building
(Qajar-1889)
Baladieh building (
Qajar-1866)
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
Fig. 17. The diagram of the evolution of the façade and the
geometric patterns based on the basic shapes. Source: authors.
facade according to the construction time (Qajar period
to the contemporary era). A horizontal comparison
shows the basic shapes that were in common in all
the buildings surrounding the square in each period.
Thus, by comparing the buildings of Baladieh, Shahi
Bank and the marching space, the presence of squares
and circle in Qajar period was made obvious. By
comparing the buildings of Baladieh (the hallway , the
Bank of Commerce, the Post and Telegraph Building,
Police ofice and the Road Administration building
in Pahlavi I Period, the bold presence of triangle
shapes was revealed. And inally by comparing the
buildings of Baldieh (the latest evolutionof the gate),
the building of Telecommunications and the Museum
of Industry in Pahlavi II, the presence of the square
shape in this period became evident.
3. Adapting the geometric patterns with the obtained
facades and identifying the process of geometric
transformations: At this stage which was the inal stage
of this research, the geometric patterns and the facades
of the existing buildings were adapted and studied. In
this process, following the adaptation of the geometric
patterns and the facades built on the north, south, east
side of the square from Qajar to contemporary time,
the followings were concluded:
A) North- Baldieh Building (Former Municipality):
1- Qajar period: In this period, when the primary
foundation of the square was established during
Nasereddin Shah Qajar’s reign, by an order of Mirza
Taghi Khan Amir Kabir in about ten years, the overall
form of the building, the apertures, and ornaments were
...........................................................
historical-cultural authenticity. Therefore, the shape
patterns derived from the geometry science have to
be studied in this paper. For this purpose, the present
research is carried out in three staged: 1. Identifying
the basic shapes, their transformations and, their
geometric derivatives: At this stage, the basic shapes
known by some scholars such as Durand and Krier
were introduced; and the square, the triangle and
the circle were deined as the basic geometric
patterns. Thereafter, the transformation principles on
the symmetry axis presented by Durand including
rotation, repetitions, relections and deletions; and
the geometric processes introduced by Krier such as
transformation, overlaying, merging, addition, sector,
and angle were applied to the shape properties such as
vertices, sides, centers, and axes in order to achieve
a certain geometric process based on geometry
principles. The resulting processes were: delection,
repetition, angle, and combination. Eventually, the
recreation of the studied shape formation processes
with respect to the geometric properties of the basic
shapes led to recognition of the geometric patterns as
referable shape patterns.
2. Identiication of the transformations in the facades
of buildings surrounding Imam Khomeini Square
(Toopkhane Square) in the four main directions, from
Qajar period to the contemporary era: At this stage, the
visual information was collected using all available
sources including books, internet sites, Tehran’s
old and current photographs, Cultural Heritage and
Tourism Organization of Tehran and various types
of visual media in the market that introduced Imam
Khomeini Square, as well as taking pictures of the
facades around the square. Thereafter a distinction
was made between explicit, referable data and
impaired, unidentiiable, misleading data. Eventually,
the data (pictures) was classiied based on the building
location (north, south, west, and east) and construction
time which was inally categorized in four periods of
Qajar, Pahlavi, Pahlavi II and contemporary era.
In this regard, the vertical and horizontal data were
compared by devising a table (Fig. 5). A vertical
comparison reveals the physical evolution of the
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29
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Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj/ Bagh- e Nazar, 14 (53):15-32
conigured using the simple circle and square sections.
Moreover, the major processes used in these shapes
were the combination of squares and circles based on
the center of the circle and the square delection based
on the axis. Subsequently, this square was turned
into Mashgh Square (infantry and cavalry marching
space) and then changed into the artillery due to the
fact that two important gates of the city were located
in this area. Therefore, the square façade was rebuilt
and a gate was added to Baladieh building which was
located on the north side of the square. At this time,
the overall form of the building, the apertures, and the
ornaments consisted of simple sections of circle and
square; alike the past period. However, this simple
combination of the circle and the square (based on the
center of the circle) was associated with the process of
changing the angle of the circle (ellipse).
Pahlavi I Period: In this period, the triangular shapes
in facades were used more often. A clock element was
added to the hallway and three processes are observed
at this stage of time; the combination of the circle and
square based on the square vertices, the combination
of the circle and square based on the vertex of the
circle, as well as the combination of the circle and
triangle.
Pahlavi II Period: having added an entrance in this
period, the clock element above the hallway was
changed and the building was completed using a
combination of complex processes. The pattern used
in the construction of the clock element above the
hallway was shaped by delection process of the circle
on its diameter as well as the angle transformation
process. Subsequently, in the last years of this period,
Baladieh underwent a different change in the hallway
and tended towards the modern architecture patterns
by the process of angle transformation from square to
rectangle.
4- The contemporary era: During this period,
Baladieh building was completely destroyed, and
shops and commercial units behind the building were
known as the buildings behind the municipality. The
abundant arrival of vehicles, as well as the expansion
of the square space, and the displacement of the
..............................................................................
30
municipality’s building were factors in the destruction
of the Baladieh building.
B) South – Military marching space, Post and
Telegraph Building, Telecommunication Building:
1- Qajar period (Military marching space): In this
period, the general forms of the arches and vaults are
created by the combination of the circle and square
based on the center of the circle. Here, the circle is turned
into an ellipse in the process of angle transformation,
by which the shape of the vaults is formed. In addition,
a new ornamental pattern is observed above the south
facade (the place for observing the parade) in which
the repetition of circles around a central circle based
on the center of the circle along with the combination
process with square is perceived.
2- Pahlavi I Period (Post and Telegraph Building): In
this period, with the advent of patterns with triangular
cross sections, triangular shapes are observed in
the façade, apertures, and the overall form of the
building such as the pediments above the entrance.
The top dome form is created by two processes: 1. the
combination of a circle and a triangle on the center of
the circle; and 2. the combination of the triangle and
the square based on the side of the square.
3- Pahlavi II Period (Telecommunication Building):
Following the advent of modern architectural
principles, the overall form of the building and apertures
are shaped by the process of angle transformation from
square to rectangle. Therefore, the telecommunication
building is characterized by patterns of Western
architecture, and particularly modern style, in a simple
cubic form, without any delection and curvature in
the building mass or diagonal and curved lines in the
façade, by having rectangular elevated windows.
4- The contemporary era: In this period, the
telecommunication building remains unaffected
without any changes in the form and the facade.
C) East- Shahi Bank, Bank of Commerce (current
Tejarat Bank):
1- Qajar period (Bank of Shahi): In this period, some
elements can be recognized after the destruction of
the initial construction and the creation of Shahi bank.
The general form of the arches is derived from the
The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj / Bagh- e Nazar, 14 (53):15-32
patterns are dominated by the process of angle and
the transformation of a square to a circle. In the road
administration building, even the overall triangular
shapes used in the building façade are created by
overlaying of rectangular shapes in form of stairs
(mastaba).
4- the contemporary era (Imam Khomeini Metro
Station): In this building, the ideas of traditional and
modern patterns are both used in the process of angle
transformation and changing of a circle into an ellipse
and a square into a rectangle. Subsequently, the shapes
were used in the façade by application of combiantion
process.
Subsequently, the geometric evolutions of the patterns
in the mentioned period are discussed. Then, the visual
documentations of each side (the facades of studied
buildings) are put in a row Fig. 10 and the geometric
patterns used in the façade are displayed respectively.
As a result, the geometric pattern transformation in
every period is achieved by putting the facades (in
terms of the overall form, apertures and ornaments),
and the geometric patterns of the facades into scrutiny.
Consequently, in this process, the geometric patterns
used in each period are introduced as their indicators
of the geometric pattern. In order to ind out which
geometric patterns are superior according to shape
approaches, a table for evaluation of geometric
patterns regarding the criteria of basic shapes was
devised. In this table, the value of the existing shapes
based on the time sequence of the human recognition
of the geometric patterns (circle, square, and triangle)
was mentioned. Hence, according to the indings and
the documents, the irst geometric shape recognized by
human beings and used in architecture was the circle,
after which the square (irregular quadrilateral) and the
triangle were known. Hence, the triangle, square and
circle have the highest and lowest values respectively.
Finally, using the geometric value table and the
classiication of geometric pattern table and the
evolution of façades around the square based on the
basic shapes (Fig. 16), the table of the value of facades
and geometric patterns in Imam Khomeini Square in
Tehran (Fig.17) is obtained.
...........................................................
simple combination of circles and squares based on
the center of the circle. As for the ornaments, the
pattern is created by the repeatition of circles around a
circle on the center of the central circle in combination
with square.
2- First Pahlavi Period (Bank of Commerce): In this
period, triangular sections and their combination with
other sections were seen in the facade and the overall
form of the buildings. In this building, the hallway form
is created by the process of angle transformation by
which square is turned into a rectangle. The products
were combined with the sections of the square and
circle. Furthermore, the angle transformation process
and changing of the square to the rectangle is observed
in the overall form of the building.
3- Pahlavi II period (Bank of Commerce): During this
period, the Bank’s building did not change.
4- The contemporary era (Tejarat Bank): In this
period, the Bank of Commerce has been renamed to
Tejarat Bank. No alterations were applied to the form
and appearance of the building other than the few
required repairs.
D) West- Police ofice, Road Administration building,
Museum of Industry building, Imam Khomeini Metro
Station
1- Qajar period: There is no vivid document of the west
side of the square in this period. Only a few historical
documents indicate that this side of the square had
entries to the place of storing ordnances (artillery)
and weapon warehouse (the place of manufacturing
weapons). It also led to Shahi (royal) mansion whose
entrance was renamed as the gate of the National
Garden in the next period.
2- Pahlavi I Period (Police ofice, Trafic ofice): In this
period, the patterns of using triangular cross sections
are observed in different dimensions, including the
roof cover. In the police ofice building, the use of
triangular cross section is not visible from the square,
and the used patterns are created through the traditional
process which is the process of combining the circle
and the square based on the square side in the form of
the vaults and arches.
3- Pahlavi II period (Trafic ofice): In this period, the
..............................................................................
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Seyed Ali Seyedian,Saeed Alinia,Vahid Heidar Nattaj/ Bagh- e Nazar, 14 (53):15-32
Summary and Conclusion
The architecture science is continuously derived from geometric principles in which the design lines are organized
in a mental process by the designer. In this regard, the application of geometric patterns has a signiicant role
in designing the plan as the building map, in scheming the façade as the building appearance, and in creating
the mass as the building form. Identifying the basic shapes and their geometric combination methods do not
go far beyond the expectations of recognizing the past used patterns. Therefore, considering the importance of
the façade design in terms of visual signiicance in architecture, it is necessary to achieve a speciic method in
design and ease the reading of the facades of valuable monuments in order to preserve the historical-cultural
authenticity. In order to achieve this goal, the shape patterns that are obtained by use of geometry are required.
The importance of recognizing the prevailing geometric pattern in each period was displayed in the presented
typology of shapes, which led to further understanding and reading of building façade. Moreover, it revealed the
importance of using geometric principles in the design which undermined mere imitational consumer-oriented
approach and highlighted the signiicant role of geometric design in architecture.
As a result, the followings are achieved in this paper by comparing and categorizing geometric patterns and their
adaptation to the transformed facades over time:
The most of the geometric patterns used in the facades of the surrounding monuments during Qajar period were
formed of simple shapes such as circles and squares or their combination according to the center of the circle
or in the process of repetition. During Pahlavi I, the triangular shapes and sections with acute angles were
appeared in a variety of combinations with circles and squares. As for the Pahlavi II period, the inluence of
Western architecture issued simplicity and prevented ornaments in various constructions of different functions.
As a result, the geometric patterns used in this period were mostly squares and the products from square
rotation in angles.
Endnote
1. Pierre-Simon Laplace (French mathematician, physicist, astronomer, and philosopher; 1827-1749)
2. Gaspard Monge (French mathematician, physicist, chemist, who researched in some branches of geometry; 1718-1818)
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Stockholm, pp. 384-392.
http: //www.iichs.org (Institute for History Studies of Contemporary Iran)
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The Scientiic Journal of NAZAR research center (Nrc) for Art, Architecture & Urbanism
Bagh-e Nazar Journal