Triakis octahedron

Triakis octahedron

(Click here for rotating model)
Type Catalan solid
Coxeter diagram
Conway notation kO
Face type V3.8.8

isosceles triangle
Faces 24
Edges 36
Vertices 14
Vertices by type 8{3}+6{8}
Symmetry group Oh, B3, [4,3], (*432)
Rotation group O, [4,3]+, (432)
Dihedral angle 147°21′00″
arccos(−3 + 8√2/17)
Properties convex, face-transitive

Truncated cube
(dual polyhedron)
Triakis octahedron Net
Net

In geometry, a triakis octahedron (or trigonal trisoctahedron[1] or kisoctahedron[2]) 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; that is, it is the Kleetope of the octahedron. It is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron. Both names reflect 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 at different relative distances from the center.

If its shorter edges have length of 1, its surface area and volume are:

  1. ^ "Clipart tagged: 'forms'". etc.usf.edu.
  2. ^ Conway, Symmetries of things, p. 284