Biaugmented triangular prism

The biaugmented triangular prism, or bautip, is one of the 92 Johnson solids (J50). It consists of 2+2+2+4 triangles and 1 square. It can be constructed by attaching square pyramids to two of the square faces of the triangular prism.

Vertex coordinates
A biaugmented triangular prism of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{2}$/6, ±1/2),
 * (0, $\sqrt{2}$/3, ±1/2),
 * (±(1+$\sqrt{3}$)/4, (3$\sqrt{6}$+$\sqrt{6}$)/12, 0).

In vertex figures
Variants of the biaugmented triangular prism by changing the edge opposite to the square appear as the vertex figure of the nonuniform antiditetragoltriate. This vertex figure has an edge length of 1 for all other edges except for the 4 edges of length $\sqrt{2}$ that are not connected to the base vertices, and has no corealmic realization.