Geometry is a branch of mathematics that deals with the properties of space about shape, size, distance, and relative position with the use of lines, points, 2D and 3D shapes, surfaces, and angles. The geometric design is about the representation and construction of free-form volume, curves, lines, and shapes for creative results. Geometric design in architecture was pioneered by Chuck Hoberman with his transformational geometry research as a design idiom. Architectural geometry is a part of research looking at the analysis, manufacturing and design processes of geometry while combining architecture and applied geometry. Architectural geometry problems lead to research and result in computer-aided geometric design, geometry processing and discrete differential geometry. Geometry is fundamental in architecture as it makes our buildings exist and aesthetically pleasing and helps in dividing space through representation on architectural plans and drawings.

Geometry history in Architecture

Geometry rules were believed to have been written first in 300BCE by Euclid of Alexandria, a Greek mathematician. It was then linked to architecture in the 20BCE by Marcus Vitruvius , a Roman architect who wrote De Architectura (Ten Books on Architecture). This book described a building’s normal proportions while relating it to the human body’s proportion; this is the basic geometry used in the built environment. Vitruvius based his architectural writing on the human body, and he studied its proportion and symmetry. This was based on his observation that human beings are shaped in a uniform and precise ratio. He found the golden ratio, which is the hidden code in architecture and life’s building blocks. In 1520 CE, the Renaissance period, De Architectura was translated by Cesare Cesariano from Latin to Italian. Leonardo da Vinci, an Italian Renaissance architect and artist, drew the ‘Vitruvian Man’ from the writings and works of Vitruvius. The Vitruvian man is represented by a human being with geometrical symbols such as squares, circles and ellipses to show man’s physical geometry through Vitruvian calculations. Another version of ten books on Architecture was written by Leon Battista Alberti. The principles focused on the use of geometry (circle) in the design of religious buildings and ensuring ratios between elements are maintained in the entire building while integrating harmonic proportion rules in his theory of architecture.

Florence Cathedral

Santa Maria Del Fiore is located in Firenze, Italy , and was designed by Filippo Brunelleschi.  The church is fully covered by coloured marbles and utilizes the Fibonacci Spiral as well as the Droste effect. The building also utilized fractal geometry, which the use of recursive pictures displayed on the dome ceiling exemplifies the Droste effect use. Florence Cathedral possesses a complex geometry through the use of ancient theories, creating a stunning monument referenced in architecture.

An overview of geometric design - Sheet1
Santa Maria del Fiore_©Bruce Stokes

Environmental Geometry in Architecture

Sacred geometry concepts have been utilized by architects to create pleasing spaces using particular geometric forms. Sacred geometry involves the belief that patterns and numbers have a sacred significance, the golden ratio is an example of sacred geometry.

The pattern can be found everywhere in nature: tree branches, snowflakes, zebra stripes, and nautilus shells.


Symmetry involves the balanced arrangement of spaces and forms to make it look equivalent at the centre. Symmetry happens by rotation or reflection of the near-repetition of a pattern element. It is prevalent in living things and can be found in animals as mirror symmetry and in some flowers and leaves of plants as rotational symmetry. The type of symmetry found in echinoderms (a marine organism) is the fivefold symmetry, and the sixfold symmetry is found in snowflakes.

Taj Mahal

The Taj Mahal is a mausoleum built by the Mughal emperor Shah Jahan between 1631 and 1648 in Agra in remembrance of Mumtaz Mahal, his wife. The structure is located in Agra District, Uttar Pradesh on a site of seventeen hectares on Yamuna River’s right bank. The building was designed by Ustad-Ahmad Lahori and is made of a mosque, an outer courtyard and a guest house. The building along a central axis emphasizes bilateral symmetry, making it a perfectly planned symmetrical building.

An overview of geometric design - Sheet2
Taj Mahal_©Kristian Bertel


Spirals are formed by points rotating around a fixed axis to an increasing distance. Spiral involves a gradual and continuous tightening curve around a central point. Spirals can be found in animals and plants, such as phyllotaxis, nautilus, and molluscs. Mathematical functions are used to define them, and they relate the distance of a point from its origin to the angle it is rotated.

Audemars Piguet Museum

The project is a museum designed for Audemars Piguet as a headquarters extension. The museum is located in Le Brassus, near Le Chenit in Switzerland , and it is a landscaped spiral glass pavilion which displays the company’s one hundred and thirty-nine-year history. Audemars Piguet Museum resembles a watch spring with two sloping spirals coiling around and includes a guest house, workspaces, and gallery spaces.

An overview of geometric design - Sheet3
Audemars Piguet Museum_©Bjarke Ingels Group


Fractals encompass similar patterns repeated at gradually smaller scales. They are self-similar patterns across varied scales and are infinitely intricate patterns. They are made by repeating a simple process in a feedback loop. Fractals exist between familiar dimensions geometrically, and nature is full of fractals. Fractal occurs a lot in nature and can be seen as clouds, seashells, mountains, snowflakes, and coastlines.

Lideta Mercato

Lideta Mercato is a shopping mall located in Addis Ababa, Ethiopia and designed by Xavier Vilalta. The design incorporated fractal geometry, with the façade influenced by beautiful patterns found on dresses of Ethiopian women. The building skin used a lightweight concrete prefab system for building, and the shape was taken from an Ethiopian traditional fractal pattern found in the local fabrics. The façade also considered the local climate conditions and created protection from the sun while regulating the ventilation and natural lighting.

An overview of geometric design - Sheet4
Lideta Mercato_©Gonzalo Guajardo


Tessellations are patterns made by the repetition of tiles on a flat surface. They are hard to find in living things but can be easily found in designs and arts. Tessellation covers a surface using geometric shapes with no gaps and overlaps. Tessellations are found in honeycombs’ wax cells, social wasps’ paper nests, salak and bony fish.


Tri-tessellate is a factory designed by Amit Khanna and located in Noida, India. The building derives its name from the tessellation (visual complexity) on the facade. Triangles made of glass panels were the shapes and materials that were repeated on the facade of this factory. The panels’ colours were selected to create better light absorption and high reflectivity levels at the lower and top levels of the building, respectively.



  1. Wikipedia contributors (2022) Geometric design , Wikipedia, The Free Encyclopedia . Available at:
  2. Wikipedia contributors (2022) Architectural geometry , Wikipedia, The Free Encyclopedia . Available at:
  3. Wikipedia contributors (2022) Geometry , Wikipedia, The Free Encyclopedia . Available at:
  4. Wikipedia contributors (2022) Patterns in nature , Wikipedia, The Free Encyclopedia . Available at:
  5. stevenaoun (2016) 1294 – 1434 Florence Cathedral , Chronology of Architecture . Available at: (Accessed: July 12, 2022).
  6. Symmetry in Architecture – Video & Lesson Transcript | (no date).
  7. UNESCO World Heritage Centre (no date) Taj Mahal , UNESCO World Heritage Centre . Available at: (Accessed: July 12, 2022).
  8. Spiral (no date) Available at: (Accessed: July 12, 2022). Read more: Spiral – Characteristics Of A Spiral, Types Of Spirals – Distance and Chapel – JRank Articles
  9. Baldwin, E. (2019) Bjarke Ingels on New Spiral Museum for Swiss Watchmaker , ArchDaily . Available at: (Accessed: July 12, 2022).
  10. What are Fractals? (no date) . Available at: (Accessed: July 12, 2022).
  11. Wikipedia contributors (2022) Fractal , Wikipedia, The Free Encyclopedia . Available at:
  12. May, K. T. (2013) Architecture infused with fractals: how TED speaker Ron Eglash inspired architect Xavier Vilalta , . Available at: (Accessed: July 12, 2022).
  13. Rojas, C. (2016) Lideta Market / Vilalta Studio , ArchDaily . Available at: (Accessed: July 12, 2022).
  14. Kizilörenli, E. and Maden, F. (2021) “Tessellation in architecture from past to present,” IOP conference series. Materials science and engineering , 1203(3), p. 032062. doi: 10.1088/1757-899x/1203/3/032062.
  15. Sagredo, R. (2018) Tri-Tessellate / AKDA , ArchDaily . Available at: (Accessed: July 12, 2022).

Chukwuebuka is an architecture student and an amateur writer using his skills to express his ideas to the world. He has written a few articles for DAPC Uniben and he is adventuring to become a popular writer.

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