Great duoantiprism

Great duoantiprism
Type	Uniform polychoron
Schläfli symbols	s{5}s{5/3} {5}⊗{5/3} h{10}s{5/3} s{5}h{10/3} h{10}h{10/3}
Coxeter diagrams
Cells	50 (3.3.3) 10 (3.3.3.5) 10 (3.3.3.5/3)
Faces	200 {3} 10 {5} 10 {5/2}
Edges	200
Vertices	50
Vertex figure	star-gyrobifastigium
Symmetry group	[5,2,5]+, order 50 [(5,2)+,10], order 100 [10,2+,10], order 200
Properties	Vertex-uniform
Net (overlapping in space)

The great duoantiprism is the only uniform star-duoantiprism solution p=5, q=5/3, in 4-dimensional geometry. It has Schläfli symbol {5}⊗{5/3}, s{5}s{5/3} or ht_0,1,2,3{5,2,5/3}, 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.

Images

stereographic projection, centered on one pentagrammic crossed-antiprism

Orthogonal projection, with vertices colored by overlaps, red, orange, yellow, green have 1, 2, 3,4 multiplicity.

Other names

• Great duoantiprism (gudap) Jonathan Bowers ^[1][2]

References

• Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
• Norman Johnson Uniform Polytopes, Manuscript (1991)
  • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
• Klitzing, Richard. "4D uniform polytopes (polychora) s5/3s2s5s - gudap".