Isoclinic Rotations

Some articles on isoclinic rotations, rotation, rotations, isoclinic:

Rotations In 4-dimensional Euclidean Space - Geometry of 4D Rotations - Isoclinic Rotations
... If the rotation angles of a double rotation are equal then there are infinitely many invariant planes instead of just two, and all half-lines from O are displaced through the ... Such rotations are called isoclinic or equiangular rotations, or Clifford displacements ... not all planes through O are invariant under isoclinic rotations only planes that are spanned by a half-line and the corresponding displaced half-line are invariant ...
Rotations In 4-dimensional Euclidean Space - Geometry of 4D Rotations - Special Property of SO(4) Among Rotation Groups in General
... The odd-dimensional rotation groups do not contain the central inversion and are simple groups ... The even-dimensional rotation groups do contain the central inversion −I and have the group C2 = {I, −I} as their centre ... there is no conjugation by any element of SO(4) that transforms left- and right-isoclinic rotations into each other ...
Rotations In 4-dimensional Euclidean Space - Geometry of 4D Rotations - Group Structure of SO(4)
... Each plane through the rotation centre O is the axis-plane of a commutative subgroup isomorphic to SO(2) ... All left-isoclinic rotations form a noncommutative subgroup S3L of SO(4) which is isomorphic to the multiplicative group S3 of unit quaternions ... All right-isoclinic rotations likewise form a subgroup S3R of SO(4) isomorphic to S3 ...