Triakis tetrahedron
In geometry, a triakis tetrahedron (or kistetrahedron) is a Catalan solid with 12 faces. Each Catalan solid is the dual of an Archimedean solid. The dual of the triakis tetrahedron is the truncated tetrahedron.
| Triakis tetrahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Catalan solid |
| Coxeter diagram | |
| Conway notation | kT |
| Face type | V3.6.6 isosceles triangle |
| Faces | 12 |
| Edges | 18 |
| Vertices | 8 |
| Vertices by type | 4{3}+4{6} |
| Symmetry group | Td, A3, [3,3], (*332) |
| Rotation group | T, [3,3]+, (332) |
| Dihedral angle | 129°31′16″ arccos(−7/11) |
| Properties | convex, face-transitive |
Truncated tetrahedron (dual polyhedron) |
Net |
The triakis tetrahedron can be seen as a tetrahedron with a triangular pyramid added to each face; that is, it is the Kleetope of the tetrahedron. It is very similar to the net for the 5-cell, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each face. This interpretation is expressed in the name.
The length of the shorter edges is 3/5 that of the longer edges. If the triakis tetrahedron has shorter edge length 1, it has area 5/3√11 and volume 25/36√2.