Triangular-square duoantiprism

The triangular-square duoantiprism or tisdap, also known as the 3-4 duoantiprism, is a convex isogonal polychoron that consists of 6 square antiprisms, 8 triangular antiprisms, and 24 digonal disphenoids. 2 square antiprisms, 2 triangular antiprisms, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the hexagonal-octagonal duoprism. However, it cannot be made uniform, as it generally has 3 different edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{24+9\sqrt2}{23}}$$ ≈ 1:1.26367.

Vertex coordinates
The vertices of a triangular-square duoantiprism, assuming that the square antiprisms are regular of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac12,\,0,\,\frac{\sqrt[4]{8}}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt[4]{72}}{4},\,-\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt[4]{8}}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt[4]{72}}{4},\,\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,-\frac{\sqrt[4]{8}}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt[4]{72}}{4},\,\frac{\sqrt[4]{8}}{4}\right).$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac12,\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac12,\,\frac{\sqrt3}{6}\right).$$