Triakis octahedron
The Triakisoktaeder is a convex polyhedron composed of 24 equilateral triangles and one of the the Catalan bodies. It is dual to the Hexaederstumpf and has 14 vertices and 36 edges.
Formation
Are applied to the eight boundary surfaces of an octahedron ( side length ) placed pyramids with the edge length, creates a Triakisoktaeder if the condition is satisfied.
- For the aforementioned minimum value of the placed pyramids have depth 0, so that only the octahedron remains with the edge length.
- The special Triakisoktaeder with the same dihedral angles formed when is.
- Assuming the above-mentioned maximum value, the Triakisoktaeder degenerates into a rhombic dodecahedron with edge length.
- Exceeds the maximum value, then the polyhedron is not convex, and finally degenerate for the star tetrahedron.