Petrial small stellated dodecahedron

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Petrial small stellated dodecahedron
Rank3
TypeRegular
SpaceSpherical
Notation
Schläfli symbol

Elements
Faces10 skew hexagons
Edges30
Vertices12
Vertex figurePentagon
Measures (edge length 1)
Circumradius
Related polytopes
ArmyIke
RegimentSissid
Petrie dualSmall stellated dodecahedron
φ 2 Petrial great icosahedron
κ ?Icosahedron
ConjugatePetrial great dodecahedron
Convex hullIcosahedron
Abstract & topological properties
Euler characteristic-8
Schläfli type{6,5}
OrientableNo
Genus10
Properties
SymmetryH3, order 120
Flag orbits1
ConvexNo
Dimension vector(1,2,2)

The Petrial small stellated dodecahedron is a regular skew polyhedron consisting of 10 skew hexagons. It is the Petrie dual of the small stellated dodecahedron, and has an Euler characteristic of -8.

Vertex coordinates[edit | edit source]

The vertices of the Petrial small stellated dodecahedron are the same as those of the small stellated dodecahedron, the regiment colonel.

Related polyhedra[edit | edit source]

The rectification of the Petrial small stellated dodecahedron is the small dodecahemicosahedron, which is uniform.

External links[edit | edit source]