Regular icosahedron Regular icosahedron In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most sides. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.3 or 3. It is the dual of the dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex. A regular icosahedron is a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of
Small stellated dodecahedron the form of doubly-wound pentagons overlapping the first 12 pentagons. The latter faces are formed by truncating the original pentagrams. When an {n/d}-gon is truncated, it becomes a {2n/d}-gon. For example, a truncated pentagon {5/1} becomes a decagon {10/1}, so truncating a pentagram {5/2} becomes a doubly-wound pentagon {10/2} (the common factor between 10 and 2 mean we visit each vertex twice to complete the polygon). Small stellated dodecahedron In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5/2,5}. It is one of four nonconvex regular polyhedra. It is composed of