Dual Solids, Morphing a Truncated Dodecahedron into a Triakis Icosahedron-Project 3

Nicole Van Oort 02/29/16 George Mason University Math 493-Mathematics Through 3D Printing Shows the morphing from the Truncated Dodecahedron to its dual the Triakis Icosahedron. The Truncated Dodecahedron is one of the 13 Archimedean Solids, meaning it is a convex polyhedron consisting of two or more regular polygons meeting at identical vertices. The Truncated Dodecahedron is composed of 20 triangles faces and 12 decagon faces, with 90 edges and 60 vertices. Polyhedra in general are paired with duels, meaning the faces of one polyhedron correspond to the vertices of another polyhedron. The group of duels to Archimedean solids are known as Catalan solids, first described in 1865 by Eugène Catalan. For the Truncated Dodecahedron, it duel or pair is the Triakis Icosahedron. This polyhedron has 60 isosceles triangle faces, with 90 edges and 32 vertices. Notice that the Truncated Dodecahedron has 32 faces, and the Triakis Icosahedron has 32 vertices. Also the Truncated Dodecahedron ha