## 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__. (http://turing.mi.ssau.ac.yu/vismath/kim/)

### 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 (http://www.arthistory.sbc.edu/sacredplaces/stpeters.html)
Tulane University, Professor Hugh Lester (http://www.tulane.edu/lester/text/Renaissance/Italian.Renaissance/Italian.Renaissance120.html)

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