Point Groups
The symmetry groups possible in a crystal lattice without the translation symmetry element. Although an isolated objectmay have an arbitrary Schönflies Symbol, the requirement that symmetry be present in alattice requires that only 1, 2, 3, and 6-fold symmetry axes are possible (the Crystallography Restriction),which restricts the number of possible point groups to 32: 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
(the Dihedral Groups), 
, 
, 
, 
,
, 
,
, 
(the Octahedral Group),
, 
, 
, 
, and 
(the Tetrahedral Group).
References
Arfken, G. ``Crystallographic Point and Space Groups.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 248-249, 1985. Cotton, F. A. Chemical Applications of Group Theory, 3rd ed. New York: Wiley, p. 379, 1990. Lomont, J. S. ``Crystallographic Point Groups.'' §4.4 in Applications of Finite Groups. New York: Dover, pp. 132-146, 1993.
- Pullback Map
- Pulse Function
- Purser's Theorem
- Pursuit Curve
- Push
- Puzzle
- P-Value
- Pyramid
- Pyramidal Frustum
- Pyramidal Number
- Pyritohedron
- Pythagoras's Constant
- Pythagoras's Theorem
- Pythagoras Tree
- Pythagorean Fraction
- Pythagorean Quadruple
- Pythagorean Square Puzzle
- Pythagorean Theorem
- Pythagorean Triad
- Pythagorean Triangle
- Pythagorean Triple
- Pépin's Test
- Pépin's Theorem
- Pólya-Burnside Lemma
- Pólya Conjecture