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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 actual symmetry groups within a frieze group are characterized by the smallest translation distance, and, for the frieze groups with vertical line reflection or 180° rotation (groups 2, 5, 6, and 7), by a shift parameter locating the reflection axis or point of rotation. In the case of symmetry groups in the plane, additional parameters ...
Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; ... Rotational symmetry; 0–9. 3-j symbol; 3D rotation group; 6-j symbol; 9-j ...
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 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 ...
The infinite series of axial or prismatic groups have an index n, which can be any integer; in each series, the nth symmetry group contains n-fold rotational symmetry about an axis, i.e., symmetry with respect to a rotation by an angle 360°/n. n=1 covers the cases of no rotational symmetry at all
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.
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.
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