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ERIC Number: EJ1100918
Record Type: Journal
Publication Date: 2016
Pages: 13
Abstractor: As Provided
ISSN: ISSN-1051-1970
Polyhedral Painting with Group Averaging
Farris, Frank A.; Tsao, Ryan
PRIMUS, v26 n4 p312-324 2016
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: California
Grant or Contract Numbers: N/A