Triakis tetrahedron

In geometry, a triakis tetrahedron (or triakistetrahedron, or kistetrahedron[1]) is a Catalan solid with 12 faces.

[2] The area, A, and volume, V, of the triakis tetrahedron, with shorter edge length "a", is equal to

Cartesian coordinates for the 8 vertices of a triakis tetrahedron centered at the origin, are the points (±⁠5/3⁠, ±⁠5/3⁠, ±⁠5/3⁠) with an even number of minus signs, along with the points (±1, ±1, ±1) with an odd number of minus signs: The length of the shorter edges of this triakis tetrahedron equals 2√2.

In modular origami, this is the result to connecting six Sonobe modules to form a triakis tetrahedron.

The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.