Petrial great icosahedron

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Petrial great icosahedron
Rank3
TypeRegular
SpaceSpherical
Notation
Schläfli symbol

Elements
Faces6 skew decagrams
Edges30
Vertices12
Vertex figurePentagram, edge length 1
Related polytopes
Petrie dualGreat icosahedron
φ 2 Petrial small stellated dodecahedron
ConjugatePetrial icosahedron
Convex hullIcosahedron
Abstract & topological properties
Flag count120
Euler characteristic-12
Schläfli type{10,5}
OrientableNo
Genus14
Properties
SymmetryH3, order 120
Flag orbits1
ConvexNo
Dimension vector(1,2,2)

The Petrial great icosahedron is a regular skew polyhedron and is the Petrie dual of the great icosahedron, so it shares its vertices and edges with the great icosahedron. It has an Euler characteristic of -12 and consists of 6 skew decagrams.

Vertex coordinates[edit | edit source]

The vertices of a Petrial icosahedron of edge length 1 centered at the origin are the same as those of the small stellated dodecahedron, its regiment colonel.

Related polyhedra[edit | edit source]

The rectification of the Petrial icosahedron is the great dodecahemidodecahedron, which is uniform.

It is abstractly equivalent to the Petrial icosahedron.

External links[edit | edit source]