Polyhedral Painting with Group Averaging. Issue 4 (21st April 2016)

• Record Type: Journal Article
• Authors: Farris, Frank A.; Tsao, Ryan
• Is Part Of: PRIMUS. Volume 26:Issue 4(2016)
• Page Start: 312
• Page End: 324
• Publication Date: 2016-04-21
• Subjects: color reversing -- group -- mathematical art -- polyhedra -- symmetry; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2015.1110218
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract: 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.