Octahedral-snub cubic honeycomb

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Octahedral-snub cubic honeycomb
Rank4
TypeUniform
SpaceHyperbolic
Notation
Bowers style acronymOctsnich
Elements
CellsN octahedra, N snub cubes
Faces8N+12N triangles, 3N squares
Edges12N+12N
Vertices3N
Vertex figureOrder-4 truncated square gyrotegum
Related polytopes
ArmyOctsnich
RegimentOctsnich
DualTetrakis square gyroprismatic honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry2B3+
ConvexYes
NatureTame

The octahedral-snub cubic honeycomb or octsnich is a convex uniform hyperbolic honeycomb that consists of snub cubes and octahedra. 2 octahedra and 8 snub cubes join at each vertex. Its vertex figure can be obtained by deleting 8 vertices from the snub cube corresponding to a square gyroprism.

This honeycomb was first discovered on February 10, 2021 and is the first and only known non-prismatic uniform to contain the snub cube as one of its cells. Its existence was confirmed by Wendy Krieger.

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