Prismatodishecatonicosachoron

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Prismatodishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymPadohi
Coxeter diagramx5/2o5o3x ()
Elements
Cells1200 triangular prisms, 720 pentagrammic prisms, 120 icosahedra, 120 small stellated dodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagrams
Edges3600+3600
Vertices1440
Vertex figurePentagonal antipodium, edge lengths 1 (large base), (5–1)/2 (small base), and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesStip–4–trip:
 Sissid–5/2–stip: 162°
 Ike–3–trip: 150°
Central density4
Number of external pieces22080
Related polytopes
ArmySemi-uniform Tex, edge lengths (icosahedra), (surrounded by truncated tetrahedra)
RegimentPadohi
ConjugateQuasiprismatodishecatonicosachoron
Abstract & topological properties
Flag count115200
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The prismatodishecatonicosachoron, or padohi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, 1200 triangular prisms, and 720 pentagrammic prisms. 1 icosahedron, 1 small stellated dodecahedron, 5 triangular prisms, and 5 pentagrammic prisms join at each vertex. It is the result of expanding the cells of either a small stellated hecatonicosachoron or a faceted hexacosichoron outwards.

The prismatodishecatonicosachoron contains the vertices of a prismatorhombisnub icositetrachoron.

Blending 10 prismatodishecatonicosachora results in the small difusiprismatosnub diprismatosnub disdishexacosichoron, which is scaliform.

Vertex coordinates[edit | edit source]

The vertices of a prismatodishecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

Related polychora[edit | edit source]

The prismatodishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms, 18 normal and 59 fissary scaliforms, and 1 scaliform compound.

o5/2o5o3o truncations
Name OBSA CD diagram Picture
Small stellated hecatonicosachoron sishi x5/2o5o3o ()
(degenerate, quadruple cover of hi) x5/2x5o3o ()
Rectified small stellated hecatonicosachoron rasishi o5/2x5o3o ()
Small hecatonicosihecatonicosachoron shihi o5/2x5x3o ()
Rectified faceted hexacosichoron rofix o5/2o5x3o ()
Truncated faceted hexacosichoron tiffix o5/2o5x3x ()
Faceted hexacosichoron fix o5/2o5o3x ()
Small rhombated small stellated hecatonicosachoron sirsashi x5/2o5x3o ()
(degenerate, sirdhi + 720(10/2)) x5/2x5x3o ()
Small rhombated faceted hexacosichoron sirfix o5/2x5o3x ()
Great rhombated faceted hexacosichoron girfix o5/2x5x3x ()
Prismatodishecatonicosachoron padohi x5/2o5o3x ()
(degenerate, six fipady + 720 double covers of pip) x5/2x5o3x ()
Prismatorhombated stellated hecatonicosachoron pirshi x5/2o5x3x ()
(degenerate, sripady + 720 double covers of pip) x5/2x5x3x ()

External links[edit | edit source]