Great duoantiprism

In geometry, the great duoantiprism is the only uniform star-duoantiprism solution $s{5}s{5/3}{5}⊗{5/3}h{10}s{5/3}s{5}h{10/3}h{10}h{10/3}$ $[5,2,5]+,$ in 4-dimensional geometry. It has Schläfli symbol $[(5,2)+,10],$ $[10,2+,10],$ or $p = 5,$ Coxeter diagram, constructed from 10 pentagonal antiprisms, 10 pentagrammic crossed-antiprisms, and 50 tetrahedra.

Its vertices are a subset of those of the small stellated 120-cell.

Construction
The great duoantiprism can be constructed from a nonuniform variant of the 10-10/3 duoprism (a duoprism of a decagon and a decagram) where the decagram's edge length is around 1.618 (golden ratio) times the edge length of the decagon via an alternation process. The decagonal prisms alternate into pentagonal antiprisms, the decagrammic prisms alternate into pentagrammic crossed-antiprisms with new regular tetrahedra created at the deleted vertices. This is the only uniform solution for the p-q duoantiprism aside from the regular 16-cell (as a 2-2 duoantiprism).

Other names

 * Great duoantiprism (gudap) Jonathan Bowers