Hollow stellated icositetrachoric hemiantiprism

The hollow stellated icositetrachoric hemiantiprism or hesihap is a prismatic uniform polyteron consisting of 48 tesseractihemioctachora, 96 pentachora as 48 stelloctangular pyramids, 48 prismatointercepted pentachora, and 48 central tetrahedral prisms; 8 tesseractihemioctachora, 10 pentachora, 10 prismatointercepted pentachora, and 8 tetrahedral prisms meet at each vertex.

Vertex coordinates
The vertices of a hollow stellated icositetrachoric hemiantiprism of edge length 1 are given by all permutations of the first four coordinates of:
 * $$\biggl(\pm\frac{1}{2},\pm\frac{1}{2},0,0,\pm\frac{\sqrt{2}}{4}\biggr)$$