Petrial octahedron

Petrial octahedron
Rank	3
Type	Regular polytope
Space	Spherical
Notation
Schläfli symbol	{6,4}3 {3,4}π
Elements
Faces	4 skew hexagons
Edges	12
Vertices	6
Vertex figure	Square (edge length 1)
Related polytopes
Petrie dual	Octahedron
Convex hull	Octahedron
Abstract properties
Flag count	48
Euler characteristic	-2
Schläfli type	{6,4}
Topological properties
Orientable	No
Genus	4
Properties
Symmetry	B3

The Petrial octahedron is a regular skew polyhedron consisting of 4 skew hexagons. It is the Petrie dual of the octahedron, therefore shares all of its edges and points with the octahedron. The Petrial octahedron has an Euler characteristic of -2.

Vertex coordinates

The vertex coordinates of a Petrial octahedron with unit side length are shared with a regular octahedron, being all permutations of:

• $\left(\pm\frac{\sqrt2}{2},\,0,\,0\right)$.

Related polyhedra

The rectification of the petrial octahedron is the cubohemioctahedron.

External links

• Wikipedia Contributors. "Petrie dual".
• Hartley, Michael. "{6,4}*48b".