Dihedrons

Trying to model the quateronion number $$ q=(t,x,y,z) $$ with a matrix is quite complex! $$ M_q = \begin{bmatrix} t+xi & y+zi \\ -y+zi & t-xi \end{bmatrix} $$

However, this is much more pleasent with dihedral math, as in $$ d = (t, x, y, z) $$ become $$ M_d = \begin{bmatrix} t + z & x+y \\ y-x & t-z \end{bmatrix} $$