The sextonions form a six dimensional algebra, intermediate between the quaternions and octonions.
J.M. Landsberg, L. Manivel, The sextonions and $E_{7 \frac{1}{2}}$, arXiv:math/0402157
Bruce Westbury, Sextonions and the magic square, (pdf)
Chandrashekar Devchand, Oxidation of self-duality to 12 dimensions and beyond, arXiv:1212.6270