# Truncated order-4 apeirogonal tiling

Truncated order-4 apeirogonal tiling
Rank3
TypeUniform, paracompact
SpaceHyperbolic
Notation
Bowers style acronymTosquazat
Coxeter diagramx∞x4o ()
Elements
FacesNM squares, 4N Apeirogons
Edges2NM+4NM
Vertices4NM
Vertex figureIsosceles triangle, edge lengths 2, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {i{\sqrt {7}}}{2}}\approx 1.32288i}$
Related polytopes
ArmyTosquazat
RegimentTosquazat
DualTetrakis order-∞ square tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[∞,4]
ConvexYes

The truncated order-4 apeirogonal tiling, or tosquazat, is a paracompact uniform tiling of the hyperbolic plane. 1 square and 2 apeirogons join at each vertex. It can be formed from the truncation of the order-4 apeirogonal tiling. It is also the cantitruncation of the order-∞ apeirogonal tiling.

## Representations

A truncated order-4 apeirogonal tiling has the following Coxeter diagrams:

• x∞x4o () (full symmetry)
• x∞x∞x () (half symmetry, apeirogons of two types)