There are 2 regular complex apeirogons, sharing the vertices of the trihexagonal tiling. Regular complex apeirogons have vertices and edges, where edges can contain 2 or more vertices. Regular apeirogons p{q}r are constrained by: 1/p + 2/q + 1/r = 1. Edges have p vertices arranged like a regular polygon, and vertex figures are r-gonal.
The first is made of triangular edges, two around every vertex, second has hexagonal edges, two around every vertex.