Triaugmented triangular prism

The triaugmented triangular prism, or tautip, is one of the 92 Johnson solids (J51). It consists of 2+6+6 triangles as faces. It can be constructed by attaching square pyramids to all three of the square faces of the triangular prism, making it topologically equivalent to the tetrakis triangular prism.

Its dual is one possible realization of the 3D associahedron.

Vertex coordinates
A triaugmented triangular prism of edge length 1 has the following vertices:
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt6}{4},\,\frac{3\sqrt2+\sqrt3}{12},\,0\right),$$
 * $$\left(0,\,-\frac{3\sqrt2+\sqrt3}{6},\,0\right).$$