Excavated dodecahedron

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Excavated dodecahedron
Rank3
TypeIsohedral
Elements
Faces60 triangles
Edges30+60
Vertices12+20
Vertex figure20 triambi, 12 pentagons
Measures (edge length 1)
Circumradius20 (6-fold):
12 (5-fold):
Volume
Number of external pieces60
Related polytopes
DualFully antitruncated icosahedron
ConjugateAugmented great stellated dodecahedron
Convex hullDodecahedron
Convex coreIcosahedron
Abstract & topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

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.

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