Hexagonal-truncated tetrahedral duoalterprism

The hexagonal-truncated tetrahedral duoalterprism, or hatuta, is a convex isogonal polyteron that consists of 12 truncated tetrahedral alterprisms, 6 digonal-hexagonal duoantiprisms, 12 hexagonal antiprismatic prisms, 8 triangular-hexagonal duoprisms, and 48 triangular cupofastegiums. 1 digonal-hexagonal duoantiprism, 1 triangular-hexagonal duoprism, 2 truncated tetrahedral cupoliprisms, 2 hexagonal antiprismatic prisms, and 4 trianguar cupofastegiums join at each vertex. It can be formed by tetrahedrally alternating the dodecagonal-small rhombicuboctahedral duoprism, so that all the small rhombicuboctahedra turn into truncated tetrahedra. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{10+4\sqrt3}{13}}$$ ≈ 1:1.14113. This occurs when it is a hull of 2 uniform hexagonal-truncated tetrahedral duoprisms.

Vertex coordinates
The vertices of a hexagonal-truncated tetrahedral duoalterprism, assuming that the edge length differences are minimized, centered at the origin, are given by: with all permutations and odd changes of sign of the first three coordinates, and with all permutations and odd changes of sign of the first three coordinates.
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{3\sqrt2}{4},\,0,\,±1\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{3\sqrt2}{4},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{3\sqrt2}{4},\,±1,\,0\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{3\sqrt2}{4},\,±\frac12,\,±\frac{\sqrt3}{2}\right),$$