Triakis icosahedron
The Triakisikosaeder is a convex polyhedron composed of 60 equilateral triangles and one of the the Catalan bodies. It is dual to the Dodekaederstumpf and has 32 vertices and 90 edges.
Formation
Will the 20 boundary surfaces of an icosahedron ( edge length ) placed pyramids with the edge length, creating a Triakisikosaeder, if the following condition is satisfied:
- For the aforementioned minimum value of the placed pyramids have depth 0, so that only the icosahedron is left with the edge length.
- The special Triakisikosaeder with the same dihedral angles formed when is.
- Assuming the above-mentioned maximum value, the Triakisikosaeder degenerates into a Rhombentriakontaeder with the edge length.
- Exceeds the maximum value, the polyhedron is not convex and finally degenerate for the Ikosaederstern.