Triakis tetrahedron
The Triakistetraeder is a convex polyhedron composed of twelve isosceles triangles and one of the the Catalan bodies. It is dual to the tetrahedron stump and has eight corners and 18 edges.
Formation
(With edge length ) placed on all four boundary faces of a tetrahedron pyramids with the edge length, creating a Triakistetraeder if the condition is met.
- For the aforementioned minimum value of the placed pyramids have depth 0, so that only the tetrahedron with an edge length remains.
- The special Triakistetraeder with the same dihedral angles formed when is.
- Assuming the above-mentioned maximum value, the Triakistetraeder degenerate into a cube with the edge length ( see chart left); this four-fold cut cubes - with an imaginary tetrahedron in the core - is topologically equivalent to Triakistetraeder.
- Exceeds the maximum value, the polyhedron is not convex and degenerates to a star body.