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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.
Category: Rotational symmetry. ... Print/export Download as PDF; ... 3D rotation group; 6-j symbol; 9-j symbol; A. Ambigram; Angular momentum coupling;
Those with reflection in the planes through the axis, with or without reflection in the plane through the origin perpendicular to the axis, are the symmetry groups for the two types of cylindrical symmetry. Any 3D shape (subset of R 3) having infinite rotational symmetry must also have mirror symmetry for every plane through the axis. Physical ...
Removing mirrors at the order-3 point creates [6,3 +], 3*3 symmetry, index 2. Removing all mirrors creates [6,3] + (632) subgroup, index 2. The communtator subgroup is [1 +,6,3 +], (333) symmetry, index 4. An index 6 subgroup constructed as [6,3*], also becomes (*333), shown in blue mirror lines, and which has its own (333) rotational symmetry ...
The body diagonal between the acute-angled vertices is the longest. By rotational symmetry about that diagonal, the other three body diagonals, between the three pairs of opposite obtuse-angled vertices, are all the same length.
There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation , Coxeter notation , [ 1 ] orbifold notation , [ 2 ] and order.
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