Great altersquare duoantiprismoid

The great altersquare duoantiprismoid, or gasdap, is a nonconvex uniform polychoron that consists of 16 cubes, 16 quasirhombicuboctahedra, 64 tetrahedra, and 64 triangular prisms. One cube, 3 quasirhombicuboctahedra, 2 tetrahedra, and 3 triangular prisms meet at each vertex.

It was discovered in April 2023; along with its conjugate it is the first uniform polychoron discovered since its colonel, the great octagonal spinoduoprism, to not share a circumradius (or much other geometry) with the small stellated hecatonicosachoron.

Unlike all other known uniforms in its regiment, the great altersquare duoantiprismoid is not a blend of uniform quasidisprismatotesseractihexadecachoron facetings.

Vertex coordinates
Its vertices are the same as those of its regiment's colonel, the great octagonal spinoduoprism.