Quasiprismatodishecatonicosachoron

From Polytope Wiki
Jump to navigation Jump to search
Quasiprismatodishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymQuipdohi
Coxeter diagramx5o5/2o3x ()
Elements
Cells1200 triangular prisms, 720 pentagonal prisms, 120 great icosahedra, 120 great dodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagons
Edges3600+3600
Vertices1440
Vertex figurePentagrammic antipodium, edge lengths 1 (small base), (1+5–1)/2 (large base), and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGike–3–trip: 150°
 Pip–4–trip:
 Gad–5–pip: 126°
Central density76
Related polytopes
ArmySemi-uniform Tex
RegimentGidipthi
ConjugatePrismatodishecatonicosachoron
Convex coreChamfered hecatonicosachoron
Abstract & topological properties
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The quasiprismatodishecatonicosachoron, or quipdohi, is a nonconvex uniform polychoron that consists of 120 great icosahedra, 120 great dodecahedra, 1200 triangular prisms, and 720 pentagonal prisms. 1 great icosahedron, 1 great dodecahedron, 5 triangular prisms, and 5 pentagonal prisms join at each vertex.

Despite its name, it is the result of expanding the cells of either a great grand hecatonicosachoron or a great faceted hexacosichoron outwards. Thus, it can also be called a great prismatodishecatonicosachoron.

Blending 10 quasiprismatodishecatonicosachora results in the great difusiprismatosnub diprismatosnub disdishexacosichoron, which is scaliform.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great dipentary trishecatonicosachoron.

Related polychora[edit | edit source]

o5o5/2o3o truncations
Name OBSA CD diagram Picture
Great grand hecatonicosachoron gaghi x5o5/2o3o ()
Truncated great grand hecatonicosachoron tigaghi x5x5/2o3o ()
Rectified great grand hecatonicosachoron ragaghi o5x5/2o3o ()
(degenerate) o5x5/2x3o ()
Rectified great faceted hexacosichoron rigfix o5o5/2x3o ()
Truncated great faceted hexacosichoron tigfix o5o5/2x3x ()
Great faceted hexacosichoron gofix o5o5/2o3x ()
Small rhombated great grand hecatonicosachoron sirgaghi x5o5/2x3o ()
(degenerate) x5x5/2x3o ()
(degenerate) o5x5/2o3x ()
(degenerate) o5x5/2x3x ()
Quasiprismatodishecatonicosachoron quipdohi x5o5/2o3x ()
(degenerate) x5x5/2o3x ()
Prismatorhombated great grand hecatonicosachoron pirgaghi x5o5/2x3x ()
(degenerate) x5x5/2x3x ()

External links[edit | edit source]