mathematics, the infinite dihedral group Dih∞ is an infinite group with properties analogous to those of the finite dihedral groups. In two-dimensional...

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the...

case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an infinite dihedral group of symmetries...

finite dihedral groups, the infinite dihedral group, and the orthogonal group O(2). Dihedral groups play an important role in group theory, geometry, and chemistry...

G is an extension of a finite group by either the infinite cyclic group or the infinite dihedral group. "Cyclic group", Encyclopedia of Mathematics,...

Another motivating example is the infinite dihedral group D ∞ {\displaystyle D_{\infty }} . This can be seen as the group of symmetries of the real line...

symmetry group. the group generated by all translations and reflections in points; they are isomorphic with the generalized dihedral group Dih(R). Up...

geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as...

D ∞ {\displaystyle D_{\infty }} , the infinite dihedral group; and one of them has three generators. The groups can be classified by their type of two-dimensional...

products will not uniquely describe an element of G. For example, the dihedral group D8 of order sixteen can be generated by a rotation, r, of order 8; and...