projections The disdyakis triacontahedron has three types of vertices which can be centered in orthogonally projection: Uses The disdyakis triacontahedron, as a regular dodecahedron with pentagons divided into 10 triangles each, is considered the "holy grail" for combination puzzles like the Rubik's cube. This unsolved problem, often called the "big chop" problem, currently has no satisfactory mechanism. It is the most significant unsolved problem in mechanical puzzles.This shape was used to make d120 dice using 3D printing. Since 2016, the Dice Lab has used the disdyakis triacontahedron to mass market an injection moulded 120 sided die. It is claimed that the d120 is the largest number of possible faces on a fair die, aside from infinite families (such as right regular prisms, bipyramids, and trapezohedra) that would be impractical in reality due to the tendency to roll for a long time. A disdyakis tricontahedron projected onto a sphere is used as the logo for Brilliant, a website containing series of lessons on STEM-related topics. Related polyhedra and tilings It is topologically related to a polyhedra sequence defined by the face configuration V4.6.2n. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any n ≥ 7. With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors. Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. This is *n32 in orbifold notation, and [n,3] in Coxeter notation. References (Section 3-9) (The thirteen semiregular convex polyhedra and their duals, Page 25, Disdyakistriacontahedron) The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 285, kisRhombic triacontahedron) External links Disdyakis triacontahedron (Hexakis Icosahedron) – Interactive Polyhedron Model Catalan solids