Regular icosahedron
In geometry, a regular icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) 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 faces.
| Regular icosahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Platonic solid |
| Elements | F = 20, E = 30 V = 12 (χ = 2) |
| Faces by sides | 20{3} |
| Conway notation | I sT |
| Schläfli symbols | {3,5} |
| s{3,4} sr{3,3} or | |
| Face configuration | V5.5.5 |
| Wythoff symbol | 5 | 2 3 |
| Coxeter diagram | |
| Symmetry | Ih, H3, [5,3], (*532) |
| Rotation group | I, [5,3]+, (532) |
| References | U22, C25, W4 |
| Properties | regular, convexdeltahedron |
| Dihedral angle | 138.189685° = arccos(−√5⁄3) |
3.3.3.3.3 (Vertex figure) |
Regular dodecahedron (dual polyhedron) |
Net | |
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 35. It is the dual of the regular dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex. In most contexts, the unqualified use of the word "icosahedron" refers specifically to this figure.
A regular icosahedron is a strictly convex deltahedron and a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of six orientations.
The name comes from Greek εἴκοσι (eíkosi) 'twenty', and ἕδρα (hédra) 'seat'. The plural can be either "icosahedrons" or "icosahedra" (/-drə/).