Pentakis icosidodecahedron
Jump to navigation
Jump to search
| Pentakis icosidodecahedron | |
|---|---|
 | |
| Rank | 3 |
| Notation | |
| Conway notation | k5aI, dcD (c = chamfer) |
| Elements | |
| Faces | 20 triangles 60 isosceles triangles |
| Edges | 60+60 |
| Vertices | 12+30 |
| Vertex figures | 12 pentagons |
| 30 rectangular-symmetric hexagons | |
| Measures (edge length 1) | |
| Central density | 1 |
| Number of external pieces | 80 |
| Level of complexity | 4 |
| Related polytopes | |
| Army | Pentakis icosidodecahedron |
| Regiment | Pentakis icosidodecahedron |
| Dual | Chamfered dodecahedron |
| Conjugate | None |
| Abstract & topological properties | |
| Flag count | 480 |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | H3, order 120 |
| Convex | Yes |
| Nature | Tame |
The pentakis icosidodecahedron is a convex polyhedron that consists of 80 triangles, 20 of which are equilateral and 60 of which are isosceles. It can be formed by augmenting pyramids onto the pentagonal faces of an icosidodecahedron.
It is usually not considered a near-miss Johnson solid, because when it is made with regular faces, some of its dihedral angles become 180°. The polyhedron then becomes an icosahedron with edges divided in half and triangular faces divided into four.
External links[edit | edit source]
- Wikipedia contributors. "Pentakis icosidodecahedron".
 | This article is a stub. You can help Polytope Wiki by expanding it. |