Apeirogon

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.

In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.

[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.

There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.