An isogonal skew apeirogon alternates two types of edges with various Frieze group symmetries.

An infinite helical (skew) polygon can exist in three dimensions, where the vertices can be seen as limited to the surface of a cylinder.

A sequence of edges of a Boerdijk–Coxeter helix can represent infinite regular helical polygons with an irrational twist angle:

A stack of right prisms can generate isogonal helical apeirogons alternating edges around axis, and along axis; for example a stack of cubes can generate this isogonal helical apeirogon alternating red and blue edges:

An infinite isogonal helical polygon with an irrational twist angle can also be constructed from truncated tetrahedra stacked like a Boerdijk–Coxeter helix, alternating two types of edges, between pairs of hexagonal faces and pairs of triangular faces: