Symmetry and Architecture*

1. http://www.mi.sanu.ac.rs/vismath/kim/index.html

Architecture, as any compositional art, makes extensive use of symmetry. Across all cultures and in all time periods, architectural compositions are symmetrically arranged. There are so many kinds of symmetry, so many kinds of architecture, and so many ways of viewing architecture, that the argument threatens to become so generalised that it loses all meaning.

The identification of symmetry types in a three-dimensional object such as a sculpture is somewhat more complicated because our perception of the object changes as we move around it. In the case of architecture, we not only move around it, but we move through it as well. This means that architecture provides us with a special opportunity to experience symmetry as well as to see it. This is possible because architecture consists of two distinct components: solid and void. Architecture is most frequently characterised by the nature of its elements: we recognise a Greek temple by its portico and pediments; a Gothic cathedral is characterised by its pointed arches and flying buttresses. These are the elements that make up the solid component of architecture, and it is likely that it is with this solid component the lay person has the most experience. Naturally in the composition of these elements that one would expect to find various kinds of symmetry relations.

Symmetry Types in Architecture
Symmetry types are divided into two categories: point groups and space groups. 
- Point groups are characterised by their relationship to at least one important reference point.
- Space groups lack such a specific reference point. 
Both point groups and space groups are found in architecture. Here are the types of symmetry found in architecture:

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http://www.slate.com/articles/arts/architecture/2008/05/mirror_images.html

Mirror Images - Why is Symmetry so Satisfying

In an early chapter of his interesting new book, Symmetry: A Journey Into the Patterns of Nature, Marcus du Sautoy describes a visit to the Alhambra, the great Moorish palace in Granada, Spain. He and his young son spend an afternoon identifying 14 different types of symmetry represented in paving patterns, ornamentation, and tile work. To the layman, the patterns may look simply like pretty forms, but to du Sautoy, who teaches mathematics at Oxford University, they are expressions of deep geometries that have their own names: gyrations, *333s, miracles, double miracles. 

Du Sautoy's book is about mathematics, but his excursion to the Alhambra is a reminder that symmetry has always been an important part of architecture. Symmetry appears in small things and large: Floor tiles may be laid in symmetrical patterns; the design of door paneling can be symmetrical, and so can window panes. In frontal symmetry, the left side of a building's facade mirrors the right (the entrance usually being in the middle); in axial-plan symmetry, the rooms on one side of the axis are a mirror image of those on the other. If the women's restroom is on one side, chances are the men's is on the other. Sometimes not being symmetrical is important; the fronts and backs of buildings, for example, are intentionally different. 

Symmetros is a Greek word, and ancient Greek architecture used symmetry as a basic organizing principle. As did Roman, Romanesque, and Renaissance. Indeed, it is hard to think of any architectural tradition, Western or non-Western, that does not include symmetry. Symmetry is something that Islamic mosques, Chinese pagodas, Hindu temples, Shinto shrines, and Gothic cathedrals have in common. 

Why is architectural symmetry so satisfying? As Leonardo da Vinci's famous drawing demonstrated, it reflects the human body, which has a right side and a left, a back and a front, the navel in the very centre. Du Sautoy writes that the human mind seems constantly drawn to anything that embodies some aspect of symmetry. He observes that "[a]rtwork, architecture and music from ancient times to the present day play on the idea of things which mirror each other in interesting ways." When we walk around a Baroque church, we experience many changing views, but when we walk down the main aisle—the line along which the mirror images of the left and right sides meet—we know that we are in a special relationship to our surroundings. And when we stand below the dome of the crossing, at the confluence of four symmetries, we know we have arrived.

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http://freshome.com/2014/09/29/why-our-brains-love-symmetry-in-design/
http://lgg.epfl.ch/publications/2008/mitra_2008_SAD.pdf