Dihedral Relation
For the rotation and reflection in , .
Lemma 1.33 (Dihedral Relation)
For where represents the rotation and represents the reflection, we have
Proof
The two sides agree on the three vertices , , and . The three-point lemma therefore gives .
Stated in
- Lemma 1.33 (Dihedral Relation)§1.7 Geometric Examples of Subgroups