A set of five icositetrachora with the same vertex arrangement of the hexacosichoron (Paulo Freire). The Zome model of the compound is the union of one pyritohedral and four prismatic projections of the icositetrachoron David Richter. Much symmetry is lost in a projection from 4D to 3D, a phenomenon called tenacious symmetry (David Richter and Scott Vorthmann) or ghost symmetry. The model has no full hexacosichoric symmetry, but pyritohedral symmetry: only 4 genuine three-fold rotational symmetry axes, 6 triagonal ghost symmetry axes and 6 pentagonal ghost symmetry axes.
This regular polychoron compound is one of the very few that are self-dual.
In the present vZome model, teal balls connecting half-blue struts avoid bending struts over each other. These appear in two flavours. Bending a b2 over a b1 is unacceptable. Bending a b2 over a b3 is also a bad idea, as the rectangular section of the b3 is oriented the wrong way (bending a b3 over a b2 would have been acceptable).
