A Polyhederal Sampler

Content Description

"The story of symmetry and color-reversing symmetry on the sphere is quite similar to the story on the Euclidean plane. It’s just a sort of round plane. The symmetries are those of the Platonic solids: tetrahedron, cube/octahedron, and dodecahedron/icosahedron. There are actually seven different types of polyhedral symmetry, allowing different mirror symmetries, as exemplified by the seven larger globes in the image. The smaller globes show color-reversing symmetry. With any color-reversing pattern we can think about what symmetries would be present if we took a color and its negative to be the same thing, as if antisymmetries were actual symmetries. On each blue path, the smaller globe has the same symmetry type as the globe at the start of the path (moving down and to the right), and would have the symmetry type of the globe at the end if you were to identify colors and their negatives." Exhibition: SymmetryScapes West: an exhibition of mathematical art.

Provenance

Purchased with the Elliot Fund and donated by the Math Department of Pacific University.

Language of Description

English

Restrictions Apply

No