Augmented triangular prism

The augmented triangular prism, or autip, is one of the 92 Johnson solids (J49). It consists of 2+2+2 triangles and 2 squares. It can be constructed by attaching a square pyramid to one of the square faces of the triangular prism.

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

In vertex figures
The augmented triangular prism appears as the vertex figure of the nonuniform digonal-triangular duoantiprism. This vertex figure has an edge length of 1, and has no corealmic realization, because the Johnson augmented triangular prism has no circumscribed sphere.

Variants made by changing the edge opposite to the vertex also appear as the vertex figure of the nonuniform duoantiprisms made out of a dyad and a regular polygon.