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Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
The lowercase letters o, s, x, and z are rotationally symmetric, while pairs such as b/q, d/p, n/u, and in some typefaces a/e, h/y and m/w, are rotations of each other. Among the lowercase letters "l" is unique since its symmetry is broken if it is close to a reference character which establishes a clear x-height. When rotated around the middle ...
Pentominoes and tetrominoes resemble (and are traditionally named after) Latin letters, and the rotation of these letterlike objects forms the basis of several games, including Tetris. Though not strict transformation, the substitution of a plural "s" with its near-reflection "z" is a fairly common trope among some minor league sports teams in ...
Symmetry (left) and asymmetry (right) A spherical symmetry group with octahedral symmetry. The yellow region shows the fundamental domain. A fractal-like shape that has reflectional symmetry, rotational symmetry and self-similarity, three forms of symmetry. This shape is obtained by a finite subdivision rule.
In this table, parentheses mark letters that stand in for themselves or for another. For instance, a rotated 'b' would be a 'q', and indeed some physical typefaces didn't bother with distinct sorts for lowercase b vs. q, d vs. p, or n vs. u; while a rotated 's' or 'z' would be itself.
Their symmetry group has two elements, the identity and a diagonal reflection. Z can be oriented in 4 ways: 2 by rotation, and 2 more for the mirror image. It has point symmetry, also known as rotational symmetry of order 2. Its symmetry group has two elements, the identity and the 180° rotation. I can be oriented in 2 ways by rotation.
C 1 is the trivial group containing only the identity operation, which occurs when the figure is asymmetric, for example the letter "F". C 2 is the symmetry group of the letter "Z", C 3 that of a triskelion, C 4 of a swastika, and C 5, C 6, etc. are the symmetry groups of similar swastika-like figures with five, six, etc. arms instead of four.
The first letter is either lowercase p or c to represent primitive or centered unit cells. The next number is the rotational symmetry, as given above. The presence of mirror planes are denoted m, while glide reflections are only denoted g. Screw axes do not exist in two-dimensional spaces.