Toroidal cycloantiprism

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Toroidal cycloantiprism
Rank4
TypeScaliform
Notation
Bowers style acronymTocap
Elements
Cells10 pentagrammic prisms
50 tetrahedra
50 square pyramids
Faces100+100 triangles
50 squares
10 pentagrams
Edges50+50+100
Vertices50
Measures (edge length 1)
Circumradius1
Hypervolume
Related polytopes
ArmyPedap
RegimentGudap
ConjugateGreat cycloantiprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)×I2(10)/2, order 200
ConvexNo
NatureTame

The toroidal cycloantiprism or tocap is a nonconvex scaliform polychoron that consists of 50 tetrahedra, 10 pentagrammic prisms, and 50 square pyramids. 4 tetrahedra, 2 pentagrammic prisms, and 5 square pyramids join at each vertex.

Related polychora[edit | edit source]

The toroidal hectosnub pyrihectosnub cycloduoantiprism, a compound of 2 toroidal cycloantiprisms, exists in a subregiment of the pentacubic extended duoantiprism.

The small dishexacosiswirlprismatic hecatonicosachoron, a compound of 12 toroidal cycloantiprisms, exists in the regiment of the small stellated hecatonicosachoron.

External links[edit | edit source]