
06618961
j
2016e.00963
Farris, Frank A.
Tsao, Ryan
Polyhedral painting with group averaging.
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 4, 312324 (2016).
2016
Taylor \& Francis, Philadelphia, PA
EN
M85
H45
color reversing
group
mathematical art
polyhedra
symmetry
doi:10.1080/10511970.2015.1110218
Summary: The technique of groupaveraging produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being wellknown in typical courses on algebra or geometry. The material makes an excellent discovery project, especially for students with some background in computer science; indeed, this is where the authors first worked through the material, as teacher and student, producing a previously unseen type of artistic image. The process uses a photograph as a palette, whose colors and textures appear in kaleidoscopic form on the surface of a sphere. We depict tetrahedral, octahedral, and icosahedral symmetries, with and without mirrors, along with the source photograph for comparison. We also describe a method to make images with colorreversing symmetry.