[1] Thorold Gosset called it a 2-dimensional semi-check, like a single row of a checkerboard.
[citation needed] If the sides are squares, it is a uniform tiling.
If colored with two sets of alternating squares it is still uniform.
[citation needed] The apeirogonal tiling is the arithmetic limit of the family of prisms t{2, p} or p.4.4, as p tends to infinity, thereby turning the prism into a Euclidean tiling.
The rectified and cantellated forms are duplicated, and as two times infinity is also infinity, the truncated and omnitruncated forms are also duplicated, therefore reducing the number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism.