We establish that there are a total of 48 distinct ordered sets of three 4×4 (skew-symmetric) signed permutation matrices which will serve as the basis of an algebra of quaternions. © 2003 Elsevier Science Inc.
Farebrother, R. W., Groß, J., & Troschke, S. O. (2003). Matrix representation of quaternions. Linear Algebra and Its Applications, 362, 251–255. https://doi.org/10.1016/S0024-3795(02)00535-9