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2. Rotation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotation_(mathematics)

   The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...

3. Rotational symmetry - Wikipedia

   en.wikipedia.org/wiki/Rotational_symmetry

   A rotocenter is the fixed, or invariant, point of a rotation. [3] There are two rotocenters per primitive cell. Together with double translational symmetry the rotation groups are the following wallpaper groups, with axes per primitive cell: p2 (2222): 4×2-fold; rotation group of a parallelogrammic, rectangular, and rhombic lattice.

4. Rotor (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotor_(mathematics)

   In mathematics, a rotor in the geometric algebra of a vector space V is the same thing as an element of the spin group Spin(V).We define this group below. Let V be a vector space equipped with a positive definite quadratic form q, and let Cl(V) be the geometric algebra associated to V.

5. Orientation (geometry) - Wikipedia

   en.wikipedia.org/wiki/Orientation_(geometry)

   The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix. The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real ...

6. Rotation - Wikipedia

   en.wikipedia.org/wiki/Rotation

   A sphere rotating (spinning) about an axis. Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation.A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.

7. Pentomino - Wikipedia

   en.wikipedia.org/wiki/Pentomino

   F, L, N, P, and Y can be oriented in 8 ways: 4 by rotation, and 4 more for the mirror image. Their symmetry group consists only of the identity mapping. T, and U can be oriented in 4 ways by rotation. They have an axis of reflection aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line ...