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:
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt6}{4},\,\\frac{3\sqrt2+\sqrt3}{12},\,0\right).$$

In vertex figures
Variants of the biaugmented triangular prism (in its symmetry axis, with non-base connected edge lengths of $\sqrt{2}$) by changing the edge opposite to the square appear as the vertex figure of the nonuniform antiditetragoltriate, and has no corealmic realization.