MATH 7210 : Foundations of Geometry II

University of Georgia, Spring 2001

Dr. McCrory, Instructor

Rotational and Reflectional Symmetry

In rotational and reflectional symmetry, there is a central point that is the center of rotation and the point of intersection of the reflection mirrors. This symmetry type is comparable to dihedral wheel patterns but can be either 2-D or 3-D.

Resource: Williams, Kim (1998). Symmetry in Architecture. (

Example 1: Pentagon

Location: Washington, D.C.

Architect: George Edwin Bergstrom

Building Type: Office building

Symmetry: The center is the building in the middle of the courtyard, and the mirrors each contain a vertex. The Pentagon is comparable to a D5 or (*5) wheel pattern.

Resource: Blackwell, William (1984). Geometry in Architecture. pg. 51.

Example 2: City of Granmichele

Location: Sicily, Italy

Architect: ???

Architecture Type: Aerial view of city layout

Symmetry: The center of this seemingly D6 or (*6) wheel pattern is the middle of the city. Three mirrors are the roads that run through the center of the city. The other three mirrors contain opposite vertices of the visibile hexagon.

Resource: Blackwell, William (1984). Geometry in Architecture. pg. 27.

Example 3: St. Peter's Basillica



Location: Vatican City, Rome, Italy

Architect: Giacomo della Porta

Building Type: Church

Symmetry: The center of this 3-D rotation is the central vertical axis through the dome. The mirrors pass through this axis, and half of them contain the blue lines (right photograph) while the other half are exactly between the blue lines. This example is comparable to a 2-D D16 or (*16) wheel pattern.

Resources: Sweet Briar College, Professor Christopher L.C.E. Whitcombe (

Tulane University, Professor Hugh Lester (

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