Order-4 square tiling honeycomb

Order-4 square tiling honeycomb
Rank	4
Type	Regular, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Sisquah
Coxeter diagram	x4o4o4o ()
Schläfli symbol	{4,4,4}
Elements
Cells	2NM square tilings
Faces	NMK squares
Edges	NMK
Vertices	2NK
Vertex figure	Square tiling, edge length √2
Measures (edge length 1)
Circumradius	0
Related polytopes
Army	Sisquah
Regiment	Sisquah
Dual	Order-4 square tiling honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[4,4,4]
Convex	Yes

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

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

• x4o4o4o (full symmetry)
• x4o4o *b4o (cells of two types)
• x4o4o4o4*a (cells of three types, x4o4x verf)
• s4o4o4o
• s4o4o *b4o
• s4o4o4o4*a

Related polytopes

o4o4o4o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Order-4 square tiling honeycomb	sisquah	{4,4,4}
Truncated order-4 square tiling honeycomb	tissish	t{4,4,4}
Rectified order-4 square tiling honeycomb = Square tiling honeycomb	squah	r{4,4,4}
Dissquare tiling honeycomb	dish	2t{4,4,4}
Rectified order-4 square tiling honeycomb = Square tiling honeycomb	squah	r{4,4,4}
Truncated order-4 square tiling honeycomb	tissish	t{4,4,4}
Order-4 square tiling honeycomb	sisquah	{4,4,4}
Small rhombated square tiling honeycomb = Rectified square tiling honeycomb	risquah	rr{4,4,4}
Great rhombated square tiling honeycomb = Truncated square tiling honeycomb	tisquah	tr{4,4,4}
Small rhombated square tiling honeycomb = Rectified square tiling honeycomb	risquah	rr{4,4,4}
Great rhombated square tiling honeycomb = Truncated square tiling honeycomb	tisquah	tr{4,4,4}
Small prismated order-4 square tiling honeycomb	spiddish	t0,3{4,4,4}
Prismatorhombated order-4 square tiling honeycomb	prissish	t0,1,3{4,4,4}
Prismatorhombated order-4 square tiling honeycomb	prissish	t0,1,3{4,4,4}
Great prismated order-4 square tiling honeycomb	dipiddish	t0,1,2,3{4,4,4}

External links

• Klitzing, Richard. "sisquah".

• Wikipedia Contributors. "Order-4 square tiling honeycomb".
• Klitzing, Richard. "sisquah".

• lllllllllwith10ls. "Category 1: Regulars" (#15).