Excavated dodecahedron
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Excavated dodecahedron | |
---|---|
Rank | 3 |
Type | Isohedral |
Elements | |
Faces | 60 triangles |
Edges | 30+60 |
Vertices | 12+20 |
Vertex figure | 20 triambi, 12 pentagons |
Measures (edge length 1) | |
Circumradius | 20 (6-fold):
12 (5-fold): |
Volume | |
Number of external pieces | 60 |
Related polytopes | |
Dual | Fully antitruncated icosahedron |
Conjugate | Augmented great stellated dodecahedron |
Convex hull | Dodecahedron |
Convex core | Icosahedron |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | H3, order 120 |
Convex | No |
Nature | Tame |
The excavated dodecahedron is an isohedral deltahedron. It can be formed by excavating every face of the regular dodecahedron with a pentagonal pyramid. It is also a non-convex variant of the pentakis dodecahedron.
This polyhedron's triangles are coplanar in sets of 3, making it superficially identical to the ditrigonal icosahedron.