\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016e.00963}
\itemau{Farris, Frank A.; Tsao, Ryan}
\itemti{Polyhedral painting with group averaging.}
\itemso{PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 4, 312-324 (2016).}
\itemab
Summary: The technique of group-averaging produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being well-known 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 color-reversing symmetry.
\itemrv{~}
\itemcc{M85 H45}
\itemut{color reversing; group; mathematical art; polyhedra; symmetry}
\itemli{doi:10.1080/10511970.2015.1110218}
\end