Augmented icosahedron

Augmented 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): ${\frac {3{\sqrt {3}}+4{\sqrt {6}}+{\sqrt {15}}}{12}}\approx 1.572257895$
Volume	$5{\frac {3+4{\sqrt {2}}+{\sqrt {5}}}{12}}\approx 4.538717595$
Number of external pieces	60
Related polytopes
Dual	Semi-uniform hypertruncated dodecahedron
Conjugate	Excavated icosahedron Augmented great icosahedron Excavated great icosahedron
Convex hull	Dodecahedron
Convex core	Semi-uniform-dual deltoidal hexecontahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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

External links

• "Isohedral Deltahedra" on orchidpalms.com