Triangular-square prismantiprismoid

The triangular-square prismantiprismoid, also known as the edge-snub triangular-square duoprism or 3-4 prismantiprismoid, is a convex isogonal polychoron that consists of 4 ditrigonal trapezoprisms, 6 tetragonal disphenoids and 12 wedges obtained through the process of edge-alternating the hexagonal-octagonal duoprism. However, it cannot be made uniform.

Vertex coordinates
The vertices of a triangular-square prismantiprismoid, assuming that the triangular antiprisms are regular and are connected by uniform triangular prisms of edge length 1, centered at the origin, are given by:
 * (0, $\sqrt{3}$/3, ±1/2, ±(3+2$\sqrt{3}$)/6),
 * (±1/2, -$\sqrt{3}$/6, ±1/2, ±(3+2$\sqrt{3}$)/6),
 * (0, -$\sqrt{3}$/3, ±(3+2$\sqrt{3}$)/6, ±1/2),
 * (±1/2, $\sqrt{3}$/6, ±(3+2$\sqrt{3}$)/6, ±1/2).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (0, $\sqrt{3}$/3, ±(2$\sqrt{6}$-3)/6, ±1/2),
 * (±1/2, -$\sqrt{3}$/6, ±(2$\sqrt{6}$-3)/6, ±1/2),
 * (0, -$\sqrt{3}$/3, ±1/2, ±(2$\sqrt{6}$-3)/6),
 * (±1/2, $\sqrt{3}$/6, ±1/2, ±(2$\sqrt{6}$-3)/6).