Partially-expanded demipenteract

The truncated tetrahedral altersquarism or tutas, also known as the digonal-truncated tetrahedral duocupoliprism, is a convex scaliform polyteron that consists of 4 truncated tetrahedral cupoliprisms, 6 hexadecachora, 12 tetrahedral prisms and 16 triangular cupolawedges formed by tetrahedrally alternating the square-small rhombicuboctahedral duoprism.

The truncated tetrahedral altersquarism can be vertex-inscribed into a small prismated demipenteract.

Vertex coordinates
The vertices of a truncated tetrahedral altersquarism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of: along with all permutations and odd sign changes of the last three coordinates of:
 * ($\sqrt{26}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (-$\sqrt{2}$/4, -$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * ($\sqrt{2}$/4, -$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (-$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)