From a Subdivided Tetrahedron to the Dodecahedron: Exploring Regular Colorings

Eva Knoll
Bridges: Mathematical Connections in Art, Music, and Science (2002)
Pages 257–261


The following paper recounts the stages of a stroll through symmetry relationships between the regular tetrahedron whose faces were subdivided into symmetrical kites and the regular dodecahedron. I will use transformations such as stretching edges and faces and splitting vertices. The simplest non-adjacent regular coloring, which illustrates inherent symmetry properties of regular solids, will help to keep track of the transformations and reveal underlying relationships between the polyhedra. In the conclusion, we will make observations about the handedness of the various stages, and discuss the possibility of applying the process to other regular polyhedra.