User:Cullinane/Shepler letter

Dear Mr. Cullinane,

Wikipedia is not a mathematics encyclopedia, correct? In that case, let me change the quote to make it more appropriate:

"The symmetry groups of the 5 Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) are generated by reflections and rotations in space. These symmetry groups are examples of reflection groups. A reflection group acts on a finite dimensional vector space and is generated by reflections: elements that fix a hyperplane in space pointwise.  Each reflecting hyperplane acts as a mirror for the reflection. Reflection groups include Weyl and Coxeter groups, complex (or pseudo) reflection groups, and groups defined over arbitrary fields.  Mathematical tools from geometry, topology, algebra, combinatorics, and representation theory are used to study reflection groups. For example, invariant theory (including modular), arrangements of hyperplanes, regular polytopes, Hecke algebras, Coxeter groups, Shephard Groups, and Braid Groups all play a prominent role in investigations on reflection groups. Reflection groups also appear in coding theory, physics, chemistry, and biology."

Best wishes, -- Anne V. Shepler

Anne V. Shepler Assistant Professor Department of Mathematics University of North Texas P.O. Box 311430 Denton, Texas 76203-1430, USA ph: 001-940-565-4943