Tetrakis hexahedron

In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube[2]) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid.

It can be called a disdyakis hexahedron or hexakis tetrahedron as the dual of an omnitruncated tetrahedron, and as the barycentric subdivision of a tetrahedron.[3]

As a Kleetope[edit]

The name "tetrakis" is used for the Kleetopes of polyhedra with square faces.[4] Hence, the tetrakis hexahedron can be considered as a cube with square pyramids covering each square face, the Kleetope of the cube. The resulting construction can be either convex or non-convex, depending on the square pyramids' height. For the convex result, it comprises twenty-four isosceles triangles.[5] A non-convex form of this shape, with equilateral triangle faces, has the same surface geometry as the regular octahedron, and a paper octahedron model can be re-folded into this shape.[6] This form of the tetrakis hexahedron was illustrated by Leonardo da Vinci in Luca Pacioli's Divina proportione (1509).[7]

https://en.wikipedia.org/wiki/Tetrakis_hexahedron