Snub cubic prism

In geometry, a snub cubic prism or snub cuboctahedral prism is a convex uniform polychoron (four-dimensional polytope).

Snub cubic prism

Schlegel diagram
TypePrismatic uniform polychoron
Uniform index56
Schläfli symbolsr{4,3}×{}
Coxeter-Dynkin
Cells40 total:

2 4.3.3.3.3
32 3.4.4
6 4.4.4

Faces136 total:
64 {3}
72 {4}
Edges144
Vertices48
Vertex figure
irr. pentagonal pyramid
Symmetry group[(4,3)+,2], order 48
Propertiesconvex

It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.

See also

  • Snub cubic antiprism s{4,3,2} - A related nonuniform polychoron

Alternative names

  • Snub-cuboctahedral dyadic prism (Norman W. Johnson)
  • Sniccup (Jonathan Bowers: for snub-cubic prism)
  • Snub-cuboctahedral hyperprism
  • Snub-cubic hyperprism
  • 6. Convex uniform prismatic polychora - Model 56, George Olshevsky.
  • Klitzing, Richard. "4D uniform polytopes (polychora) s3s4s x - sniccup".


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