There are higher dimensional algebras, too. We have:
4-dimensional quaternions,
8-dimensional octonions,
16-dimensional sedenions,
32-dimensional trigintaduonions,
64-dimensional sexagintaquattuornions,
128-dimensional centumduodetrigintanions,
256-dimensional ducentiquinquagintasexions
Who knows, maybe reality is explained by even higher dimensional systems. The 32 dimensional algebra ends with "onion," so that's my pick.
