Triangular-square duoantiprismatic antiprism

The triangular-square duoantiprismatic antiprism, or tisdapap, is a convex isogonal polyteron that consists of 2 triangular-square duoantiprisms, 6 digonal-square duoantiprisms, 8 digonal-triangular duoantiprisms, and 48 digonal disphenoidal pyramids. 1 triangular-square duoantiprism, 2 digonal-square duoantiprisms, 2 digonal-triangular duoantiprisms, and 5 digonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the hexagonal-octagonal duoprismatic prism. However, it cannot be made uniform.

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 duoantiprismatic antiprism, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt2}{2},\,0,\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt2}{2},\,0,\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac12,\,±\frac12,\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12,\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac12,\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12,\,-\frac{\sqrt6}{6}\right).$$