Great duoantiprism

The great duoantiprism or gudap, also known as the pentagonal-pentagrammic crossed duoantiprism or 5-5/3 duoantiprism, is a nonconvex uniform polychoron that consists of 50 tetrahedra, 10 pentagonal antiprisms, and 10 pentagrammic retroprisms. 4 tetrahedra, 2 pentagonal antiprisms, and 2 pentagrammic retroprisms join at each vertex.

Great duoantiprism
Gudap.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGudap
Info
Coxeter diagrams10o2s10/3o
SymmetryI2(10)×I2(10)/2, order 200
ArmyPentagonal-pentagonal duoantiprism
RegimentGudap
Elements
Vertex figureSemicrossed gyrobifastigium, edge lengths (5-1)/2, 1 and (5+1)/2
Cells50 tetrahedra, 10 pentagonal antiprisms, 10 pentagrammic retroprisms
Faces100+100 triangles, 10 pentagons, 10 pentagrams
Edges50+50+100
Vertices50
Measures (edge length 1)
Circumradius1
Hypervolume
Dichoral anglesStarp–5/2–starp: 144°
 Starp–3–tet:
 Pap–5–pap: 72°
 Pap–3–tet:
Central density3
Euler characteristic0
Number of pieces600
Level of complexity144
Related polytopes
DualPentagonal-pentagrammic concave duoantitegum
ConjugateGreat duoantiprism
Properties
ConvexNo
OrientableYes
NatureTame

It is one of only two members of the infinite set of duoantiprisms that can be made uniform, the other being the hexadecachoron. It can be obtained through the process of alternating a non-uniform decagonal-decagrammic duoprism where the decagrams have an edge length of times that of its decagons.

The great duoantiprism can be vertex-inscribed into a small stellated hecatonicosachoron. In fact it occurs as a subsymmetrical faceting of that polychoron, with the pentagrammic retroprisms being facetings of a ring of 10 small stellated dodecahedral cells.

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