Order-4 square tiling honeycomb

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Order-4 square tiling honeycomb
Rank4
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymSisquah
Coxeter diagramx4o4o4o ()
Schläfli symbol{4,4,4}
Elements
Cells2NM square tilings
FacesNMK squares
EdgesNMK
Vertices2NK
Vertex figureSquare tiling, edge length 2
Measures (edge length 1)
Circumradius0
Related polytopes
ArmySisquah
RegimentSisquah
DualOrder-4 square tiling honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry[4,4,4]
ConvexYes

The order-4 square tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. 4 ideal square tilings meet at each edge. All vertices are ideal points at infinity, with infinitely many square tilings meeting at each vertex in a square tiling arrangement.

Representations[edit | edit source]

The order-4 square tiling has the following Coxeter diagrams:

  • x4o4o4o () (full symmetry)
  • x4o4o2o4*b () (cells of two types)
  • x4o4o4o4*a () (cells of three types, small rhombated square tiling verf)
  • s4o4o4o ()
  • s4o4o2o4*b ()
  • s4o4o4o4*a ()

External links[edit | edit source]