Petrial small stellated dodecahedron

Petrial small stellated dodecahedron
Rank	3
Type	Regular
Space	Spherical
Notation
Schläfli symbol	{5/2,5}π; {6,5}5/2
Elements
Faces	10 skew hexagons
Edges	30
Vertices	12
Vertex figure	Pentagon
Measures (edge length 1)
Circumradius
Related polytopes
Regiment	Sissid
Petrie dual	Small stellated dodecahedron
Conjugate	Petrial great dodecahedron
Convex hull	Icosahedron
Abstract properties
Euler characteristic	-8
Schläfli type	{6,5}
Topological properties
Orientable	No
Genus	10
Properties
Symmetry	H3, order 120
Convex	No

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 the small stellated dodecahedron, the regiment colonel.

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

v t e Regular polyhedron
Convex polyhedra	Tetrahedron Cube Octahedron Dodecahedron Icosahedron
Euclidean tilings	Triangular tiling Square tiling Hexagonal tiling
Kepler-Poinsot solids	Great dodecahedron Small stellated dodecahedron Great icosahedron Great stellated dodecahedron
Pure apeirohedra	Mucube Muoctahedron Mutetrahedron
Hyperbolic tilings	Pentagonal tiling Heptagonal tiling Stellated heptagonal tiling Great heptagonal tiling Octagonal tiling Enneagonal tiling Stellated enneagonal tiling Great enneagonal tiling Apeirogonal tiling Order-4 hexagonal tiling Order-4 apeirogonal tiling Order-5 square tiling Order-5 pentagonal tiling Order-5 hexagonal tiling Order-5 apeirogonal tiling Order-6 square tiling Order-6 pentagonal tiling Order-6 hexagonal tiling Order-6 apeirogonal tiling Order-7 triangular tiling Order-8 triangular tiling Order-9 triangular tiling Order-∞ triangular tiling Order-∞ square tiling Order-∞ pentagonal tiling Order-∞ hexagonal tiling Order-∞ apeirogonal tiling
Petrials	Petrial tetrahedron Petrial cube Petrial octahedron Petrial dodecahedron Petrial icosahedron Petrial great dodecahedron Petrial small stellated dodecahedron Petrial great icosahedron Petrial great stellated dodecahedron Petrial square tiling Petrial triangular tiling Petrial hexagonal tiling Petrial mucube Petrial muoctahedron Petrial mutetrahedron