Crystallography Restriction
If a discrete Group of displacements in the plane has more than one center of rotation, then the only rotationsthat can occur are by 2, 3, 4, and 6. This can be shown as follows. It must be true that the sum of the interior anglesdivided by the number of sides is a divisor of 360°.
where
is an Integer. Therefore, symmetry will be possible only for
where
is an Integer. This will hold for 1-, 2-, 3-, 4-, and 6-fold symmetry. That it does not hold for 
isseen by noting that 
corresponds to 
. The 
case requires that 
(impossible), and the 
case requires that 
(also impossible).See also Point Groups, Symmetry- Polyhedron
- Polyhedron Coloring
- Polyhedron Compound
- Polyhedron Dissection
- Polyhedron Dual
- Polyhedron Hinging
- Polyhedron Packing
- Polyhex
- Polyiamond
- Polyking
- Polylogarithm
- Polymorph
- Polynomial
- Polynomial Bar Norm
- Polynomial Bracket Norm
- Polynomial Curve
- Polynomial Factor
- Polynomial Norm
- Polynomial Remainder Theorem
- Polynomial Ring
- Polynomial Root
- Polynomial Series
- Polyomino
- Polyomino Tiling
- Polyplet