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

Rotations In 4-dimensional Euclidean Space - Geometry of 4D Rotations - Special Property of SO(4) Among Rotation Groups in General

... The odd-dimensional

... 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 ... 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 -

... If the

**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 same angle ... Such**rotations**are called**isoclinic**or equiangular**rotations**, or Clifford displacements ... Beware 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 - Group Structure of SO(4)

... Each plane through the

... 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 ...