# Petrial great icosahedron

Petrial great icosahedron
Rank3
TypeRegular
SpaceSpherical
Notation
Schläfli symbol${\displaystyle \{3,5/2\}^\pi}$
${\displaystyle \{10/3,5/2\}_3}$
Elements
Faces6 skew decagrams
Edges30
Vertices12
Vertex figurePentagram, edge length 1
Related polytopes
Petrie dualGreat icosahedron
ConjugatePetrial icosahedron
Convex hullIcosahedron
Abstract properties
Flag count120
Euler characteristic-12
Schläfli type{10,5}
Topological properties
OrientableNo
Genus14
Properties
ConvexNo

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

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

## Related polyhedra

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