Back Tetràedre triakis Catalan Triakistetraeder German Τριάκις τετράεδρο Greek Trilateropiramidigita kvaredro Esperanto Triaquistetraedro Spanish Triakistetraedro Basque دوازدهمثلث وجهی Persian Triakitétraèdre French Triacistetraedro Italian 三方四面体 Japanese
| 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 |
In geometry, a triakis tetrahedron (or kistetrahedron[1]) 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.
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.[2] If the triakis tetrahedron has shorter edge length 1, it has area 5/3√11 and volume 25/36√2.
- ^ Conway, Symmetries of things, p.284
- ^ "Triakis Tetrahedron - Geometry Calculator".