Petrial great icosahedron

Petrial great icosahedron
Rank	3
Type	Regular
Space	Spherical
Notation
Schläfli symbol	$\{3,5/2\}^\pi$ $\{10/3,5/2\}_3$
Elements
Faces	6 skew decagrams
Edges	30
Vertices	12
Vertex figure	Pentagram, edge length 1
Related polytopes
Petrie dual	Great icosahedron
Conjugate	Petrial icosahedron
Convex hull	Icosahedron
Abstract properties
Flag count	120
Euler characteristic	-12
Schläfli type	{10,5}
Topological properties
Orientable	No
Genus	14
Properties
Convex	No

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.

External links

• Wikipedia Contributors. "Petrie dual".