Rectified octahedral honeycomb

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Rectified octahedral honeycomb
Rank4
TypeUniform, paracompact
SpaceHyperbolic
Notation
Bowers style acronymRocth
Coxeter diagramo4o4x3o ()
Elements
CellsNM cuboctahedra, 6N square tilings
Faces4NM triangles, 6NM squares
Edges12NM
Vertices3NM
Vertex figureSquare prism, edge lengths 2 (base) and 1 (side) 75px
Measures (edge length 1)
Circumradiusi
Related polytopes
ArmyRocth
RegimentRocth
Abstract & topological properties
OrientableYes
Properties
Symmetry[4,4,3]
ConvexYes

The rectified octahedral honeycomb is a paracompact quasiregular tiling of 3D hyperbolic space. 2 square tilings and 4 cuboctahedra meet at each vertex. It is paracompact because it has Euclidean square tiling cells. As the name suggests, it can be derived by rectification of the octahedral honeycomb.

Representatoins[edit | edit source]

A rectified octahedral honeycomb has the following Coxeter diagrams:

  • o4o4x3o () (full symmetry)
  • o4x4o *b3o () (half symmetry, cuboid verf)
  • x3o3x4o4*a () (rectangular trapezoprism verf)

External links[edit | edit source]