Small rhombated faceted hexacosichoron

From Polytope Wiki
Jump to navigation Jump to search
Small rhombated faceted hexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSirfix
Coxeter diagramo5/2x5o3x ()
Elements
Cells720 pentagrammic prisms, 120 dodecadodecahedra, 120 small rhombicosidodecahedra
Faces1200 triangles, 3600 squares, 1440 pentagons, 1440 pentagrams
Edges3600+7200
Vertices3600
Vertex figureWedge, edge lengths (1+5)/2 (two edges of base rectangle), (5–1)/2 (other 2 base edges), 2 (side edges), and 1 (top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesDid–5/2–stip: 162°
 Srid–4–stip:
 Srid–5–did: 144°
 Srid–3–srid: 120°
Related polytopes
ArmySemi-uniform Srix, edge lengths (icosidodecahedra), 1 (main triangles)
RegimentSirfix
ConjugateQuasirhombated great faceted hexacosichoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count129600
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small rhombated faceted hexacosichoron, or sirfix, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 dodecadodecahedra, and 120 small rhombicosidodecahedra. 1 dodecadodecahedron, 2 pentagrammic prisms, and 2 small rhombicosidodecahedra join at each vertex. it can be obtained by cantellating the faceted hexacosichoron.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small rhombated faceted hexacosichoron of edge length 1 are given by all permutations of:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,

together with all even permutations of:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Related polychora[edit | edit source]

The small rhombated faceted hexacosichoron is the colonel of a regiment of 7 members. Its other members include the small retrosphenoverted trishecatonicosachoron, rhombic small hecatonicosihecatonicosachoron, small pseudorhombic hecatonicosihecatonicosachoron, grand rhombic dishecatonicosachoron, small dishecatonicosintercepted dishecatonicosachoron, and hecatonicosintercepted prismatodishecatonicosachoron.

External links[edit | edit source]