Quaternions and spatial rotation of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented
Allied Masonic Degrees equivalent of the Allied Masonic Degrees, nor are the degrees for which it is responsible carried out under the auspices of any of the Scottish masonic bodies, although the 'Red Cross of Babylon' is a truncated version of the Scottish 'Babylonish Pass' degree under the control of the Supreme Grand Royal Arch Chapter of Scotland. There is no reciprocal agreement on intervisitation in the 'Lodge & Council' degrees between the Supreme Grand Royal Arch Chapter of Scotland and the Council of the Allied Masonic Degrees. Nonetheless, "The Grand Council of the Allied Masonic Degrees of England and Wales and Districts