Augmented great stellated dodecahedron

Augmented great stellated dodecahedron
Rank	3
Type	Isohedral
Elements
Faces	60 triangles
Edges	30+60
Vertices	12+20
Vertex figure	20 triambi, 12 pentagrams
Measures (edge length 1)
Circumradius	20 (6-fold): ${\frac {{\sqrt {15}}-{\sqrt {3}}}{4}}\approx 0.53523313466$ 12 (5-fold): ${\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95105651630$
Volume	${\frac {5{\sqrt {5}}-5}{4}}\approx 1.5450849719$
Number of external pieces	180
Related polytopes
Dual	Degenerate truncated great icosahedron
Conjugate	Excavated dodecahedron
Convex hull	Icosahedron
Convex core	Icosahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The augmented great stellated dodecahedron is an isohedral deltahedron. It can be formed by augmenting every face of the regular great stellated dodecahedron with a pentagrammic pyramid.

This polyhedron's triangles are coplanar in sets of 3, making it superficially identical to the great icosahedron.

External links

• "Isohedral Deltahedra" on orchidpalms.com