Triakis octahedron  

(Click here for rotating model) 

Type  Catalan solid 
Face type  isosceles triangle 
Faces  24 
Edges  36 
Vertices  14 
Vertices by type  8{3}+6{8} 
Face configuration  V3.8.8 
Symmetry group  O_{h} or *432 
Dihedral angle  147°21'0" 
Properties  convex, facetransitive 
Truncated cube (dual polyhedron) 
Net 
In geometry, a triakis octahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube.
It can be seen as an octahedron with triangular pyramids added to each face, and is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron. Both names reflect the fact that it has three triangular faces for every face of an octahedron. The tetragonal trisoctahedron is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron.
This convex polyhedron is topologically similar to the concave stellated octahedron. They have the same face connectivity, but the vertices are in different relative distances from the center.
It is also called the small triakis octahedron, so as to differentiate it from the great triakis octahedron, the dual of the stellated truncated hexahedron.
If its shorter edges have length 1, its surface area is and its volume is .

