Stelladodecahedron cone

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Stelladodecahedron cone
Rank3
Notation
Bowers style acronymSadcone
Elements
Faces5 triangles, 5 pentagrams
Edges5+5+10
Vertices1+5+5
Vertex figures1 pentagon, edge length (5–1)/2
 5 butterflies, edge lengths 1 and (5–1)/2
 5 isosceles triangles, edge lengths 1, (5–1)/2, (5–1)/2
Measures (edge length 1)
Circumradius
Dihedral angles5/2–5/2:
 3–5/2 #1:
 3–5/2 #2:
Related polytopes
ArmyGyepip, edge length
RegimentSadcone
ConjugateGreat dodecahedron cone
Convex hullGyroelongated pentagonal pyramid
Abstract & topological properties
Flag count80
Euler characteristic1
OrientableNo
Genus1
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

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

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the small stellated dodecahedron with any 1 vertex removed.

External links[edit | edit source]