Excavated icosahedron

Excavated icosahedron
Rank	3
Type	Isohedral
Elements
Faces	60 triangles
Edges	30+60
Vertices	12+20
Vertex figure	12 pentambi, 20 triangles
Measures (edge length 1)
Circumradius	12 (10-fold): ${\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.9510565163$ 20 (3-fold): ${\frac {4{\sqrt {6}}-3{\sqrt {3}}-{\sqrt {15}}}{12}}\approx 0.06073526685$
Volume	$5{\frac {4{\sqrt {2}}-3-{\sqrt {5}}}{12}}\approx 0.1753276133$
Number of external pieces	120
Related polytopes
Dual	Semi-uniform truncated dodecahedron
Conjugate	Augmented icosahedron Augmented great icosahedron Excavated great icosahedron
Convex hull	Icosahedron
Convex core	Semi-uniform-dual pentakis dodecahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The excavated icosahedron is an isohedral deltahedron. It can be formed by excavating every face of the regular icosahedron with a tetrahedron. It is also a non-convex variant of the triakis icosahedron.

As the dihedral angle of the icosahedron is slightly less than twice that of the tetrahedron, it is self-intersecting.

External links

• "Isohedral Deltahedra" on orchidpalms.com