is a realization of the abstract apeirogon.

Symmetries

The infinite dihedral group G of symmetries of a regular geometric apeirogon is generated by two reflections, the product of which translates each vertex of P to the next. The product of the two reflections can be decomposed as a product of a non-zero translation, finitely many rotations, and a possibly trivial reflection.

In an abstract polytope, a flag is a collection of one face of each dimension, all incident to each other (that is, comparable in the partial order);

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