The Triakis Octahedron
The faces are transitive; isosceles triangles with two short edges and a long edge with a (2−√2) : 1 length ratio, or approximately 0.586 : 1.
The following are images of the triakis octahedron from various viewpoints:
Front view, centered on axial vertex.
Side view, centered on a long edge.
Octant view, centered on a cube vertex.
Here's an animation of a triakis octahedron rotating around the vertical axis:
The Cartesian coordinates for the triakis octahedron are all permutations of coordinate and changes of sign of:
- (0, 0, 1+√2)
- (1, 1, 1)
These coordinates correspond with a dual truncated cube of edge length (6−4√2).