It is represented by the Schläfli symbol {∞,3}, having three regular apeirogons around each vertex.
The order-2 apeirogonal tiling represents an infinite dihedron in the Euclidean plane as {∞,2}.
There are 15 small index subgroups (7 unique) constructed from [(∞,∞,∞)] by mirror removal and alternation.
A larger subgroup is constructed [(∞,∞,∞*)], index 8, as (∞*∞∞) with gyration points removed, becomes (*∞∞).
This tiling is topologically related as a part of sequence of regular polyhedra with Schläfli symbol {n,3}.