Great duoantiprism

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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 CDel node h.pngCDel 5.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node h.png
CDel node.pngCDel 10.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node h.png
CDel node h.pngCDel 5.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 10.pngCDel rat.pngCDel 3x.pngCDel node.png
CDel node.pngCDel 10.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 10.pngCDel rat.pngCDel 3x.pngCDel node.png
Cells 50 (3.3.3) Tetrahedron.png
10 (3.3.3.5)Pentagonal antiprism.png
10 (3.3.3.5/3)Pentagrammic crossed antiprism.png
Faces 200 {3}
10 {5}
10 {5/2}
Edges 200
Vertices 50
Vertex figure Great duoantiprism verf.png
star-gyrobifastigium
Symmetry group [5,2,5]+, order 50
[(5,2)+,10], order 100
[10,2+,10], order 200
Properties Vertex-uniform
Great duoantiprism net.png
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 ht0,1,2,3{5,2,5/3}, Coxeter diagram CDel node h.pngCDel 5.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node h.png, 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).

Images[]

Great duoantiprism.png
stereographic projection, centered on one pentagrammic crossed-antiprism 		Gudap orthogonal projection.png
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[]

  1. ^ Jonathan Bowers - Miscellaneous Uniform Polychora 965. Gudap
  2. ^ http://www.polychora.com/12GudapsMovie.gif Animation of cross sections
  • 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".
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