Triangular Symmetry Group
Alternate name
Definition
Given a triangle with angles (π/p, π/q, π/r), the resulting symmetry group is called a (p, q, r) triangle group (also known as a spherical tessellation). In three dimensions, such groups must satisfy 1/p + 1/q + 1/r>1, and so the only solutions are (2, 2, n), (2, 3, 3), (2, 3, 4), and (2, 3, 5). The group (2, 3, 6) gives rise to the semiregular planar tessellations of types 1, 2, 5, and 7. The group (2, 3, 7) gives hyperbolic tessellations.
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