Triangular Symmetry Group
Given a Triangle with angles (
, 
, 
), the resulting symmetry Group is called a 
triangle group (also known as a Spherical Tessellation). In 3-D, such Groups must satisfy
and so the only solutions are
, 
, 
, and 
(Ball and Coxeter 1987). The group 
gives rise to the semiregular planar Tessellations of types 1, 2, 5, and 7. The group 
gives hyperbolic tessellations.See also Geodesic Dome
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 155-161, 1987. Coxeter, H. S. M. ``The Partition of a Sphere According to the Icosahedral Group.'' Scripta Math 4, 156-157, 1936. Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973. Kraitchik, M. ``A Mosaic on the Sphere.'' §7.3 in Mathematical Recreations. New York: W. W. Norton, pp. 208-209, 1942.
- Linkage
- Link Diagram
- Linking Number
- Links Curve
- Linnik's Constant
- Linnik's Theorem
- Lin's Method
- Liouville Function
- Liouville Measure
- Liouville Number
- Liouville Polynomial Identity
- Liouville-Roth Constant
- Liouville's Boundedness Theorem
- Liouville's Conformality Theorem
- Liouville's Conic Theorem
- Liouville's Constant
- Liouville's Elliptic Function Theorem
- Liouville Space
- Liouville's Phase Space Theorem
- Liouville's Rational Approximation Theorem
- Liouville's Sphere-Preserving Theorem
- Lipschitz Condition
- Lipschitz Function
- Lipschitz's Integral
- Lissajous Curve