Triakis octahedron

This convex polyhedron is topologically similar to the concave stellated octahedron.

If its shorter edges have length of 1, its surface area and volume are: Let α = √2 − 1, then the 14 points (±α, ±α, ±α) and (±1, 0, 0), (0, ±1, 0) and (0, 0, ±1) are the vertices of a triakis octahedron centered at the origin.

The faces are isosceles triangles with one obtuse and two acute angles.

The triakis octahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.

The triakis octahedron is also a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.