Apeirogonal prism

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.

It is also called an infinite square prism. 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.

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
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