Explore: Rotation Groups

In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space

axis, n perpendicular 2-fold axes: the dihedral groups Dn of order 2n (n ≥ 2). This is the rotation group of a regular prism, or regular bipyramid. Although

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention

special orthogonal group of order 4. In this article rotation means rotational displacement. For the sake of uniqueness, rotation angles are assumed to

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest

of SO(3), are: the cyclic groups Cn (the rotation group of a canonical pyramid), the dihedral groups Dn (the rotation group of a uniform prism, or canonical

its elements are the usual rotations around a point (in dimension 2) or a line (in dimension 3). In low dimension, these groups have been widely studied

into chiral (or purely rotational) groups and achiral groups. The chiral groups are subgroups of the special orthogonal group SO(d): they contain only

the strip, and 180° rotations. There are seven frieze groups, listed in the summary table. Many authors present the frieze groups in a different order

Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an axis of rotation. A plane figure can rotate