Great dodecahedron cone

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Great dodecahedron cone
Rank3
Notation
Bowers style acronymGadcone
Elements
Faces5 triangles, 5 pentagons
Edges5+5+10
Vertices1+5+5
Vertex figures1 pentagram, edge length (1+5)/2
 5 butterflies, edge lengths 1 and (1+5)/2
 5 isosceles triangles, edge lengths 1, (1+5)/2, (1+5)/2
Measures (edge length 1)
Circumradius
Dihedral angles3–5 #1:
 5–5:
 3–5 #2:
Related polytopes
ArmyGyepip
RegimentGadcone
ConjugateStelladodecahedron cone
Convex hullGyroelongated pentagonal pyramid
Abstract & topological properties
Flag count80
Euler characteristic1
OrientableNo
Genus1
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

The great dodecahedron cone, or gadcone, is a nonconvex orbiform polyhedron and an edge-faceting of the icosahedron. Its faces are 5 pentagons and 5 triangles. It is named as such because the 5 pentagons are arranged around one vertex similar to the configuration found in the great dodecahedron.

It is the 5-5-3 acrohedron generated by Green's rules.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the icosahedron with any 1 vertex removed, which is equivalent to those of the gyroelongated pentagonal pyramid.

External links[edit | edit source]