# Symmetry At The Cathedral Basilica of St. Louis

In 1922, and again in 1936, the Dutch artist
M. C. Escher visited the
Alhambra, in
Granada, Spain, a fourteenth century Moorish palace renowned for its
decorative artwork. He (with his wife) made sketches of numerous wall
tilings, sketches that he later used as sources for his own mathematical
art.
In St. Louis, we are lucky have some of the
finest mosaic artwork in North America, at the
Cathedral Basilica of St. Louis.
For a few years, Saint Louis University's
MATH 124: Math and the Art of M. C. Escher
course has punctuated their study of symmetries with a pilgrimage to the Cathedral to
search for mathematical symmetries in the many mosaics.

Mathematicians group flat patterns into three types: Rosette, Frieze, and Wallpaper.
These correspond to patterns with no translational symmetry, one direction of translational
symmetry (a strip), and many directions of translational symmetry.
For a basic introduction to symmetries and symmetry groups,
see Math and the Art of M.C. Escher.
The cathedral has many examples of rosette symmetries, examples of all seven possible frieze
symmetries, and some of the seventeen possible wallpaper symmetries.

### Examples from the Cathedral

Updated
.
Maintained by Dr. Bryan Clair