The unit sphere was considered in 1910 by Hans Beck.Hans Beck (1910) Ein Seitenstück zur Mobius'schen Geometrie der Kreisverwandschaften, Transactions of the American Mathematical Society 11 For example, the dihedral group appears on page 419. The split-quaternion structure has also been mentioned briefly in the Annals of Mathematics.A. A. Albert (1942), "Quadratic Forms permitting Composition", Annals of Mathematics 43:161 to 77Valentine Bargmann (1947), "Irreducible unitary representations of the Lorentz Group", Annals of Mathematics 48: 568–640
