Apeirogonal prism

Apeirogonal prism
Type	Regular tiling
Vertex configuration	4.4.∞
Schläfli symbol(s)	t{2,∞}
Wythoff symbol(s)	2 ∞ | 2
Coxeter-Dynkin(s)
Symmetry	*22 [∞,2,2], *∞2
Dual	Rectangular double row
Properties	Vertex-transitive, edge-transitive, face-transitive
4.4.∞

In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane.

Thorold Gosset called it a 2-dimensional semi-check, like a single row of a checkerboard.

If the sides are squares, it is a uniform tiling. In general, it can have two sets of alternating congruent rectangles.

Related tilings

An alternation operation can create an apeirogonal antiprism composed of three triangles and one apeirogon at each vertex.

References

• T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
• Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman and Company. ISBN 0-7167-1193-1.