Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees, and Perceptrons.
It is created by a Wythoff construction upon a set of 8 hyperplane mirrors in 8-dimensional space, defined by root vectors of the Coxeter group.
With Claudio Procesi: Topics in Hyperplane Arrangements, Polytopes and Box-Splines, Springer, 2010
a Scorza variety of dimension n in projective space of dimension 3n/2 + 2 that can be isomorphically projected to a hyperplane.
For instance, the traditional electro-static force described by Coulomb's law may be pictured in a simultaneous hyperplane, but relativistic relations of charge and force involve retarded potentials.