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triakis octahedron
In geometry, a triakis octahedron (or kisoctahedron〔Conway, Symmetries of things, p.284〕) 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 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.
If its shorter edges have length 1, its surface area and volume are:
:
==Orthogonal projections==
The ''triakis octahedron'' has three symmetry positions, two located on vertices, and one mid-edge:
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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