How E₅ = D₅, its twisted form, and the finite orthogonal groups D₅(2) and ²D₅(2) link the exceptional series E₆, E₇, E₈ to finite orthogonal holonomy and to sporadic symmetry in the Monster and Fischer groups.

Polygons, polyhedra, polytopes and their symmetry families read as routes through a landscape of finite informational forms: how a finite structure acquires, preserves, transforms, constrains, or loses symmetry through growth, contraction, skewness, and transport.

A particularly promising way to begin is to construct one finite informational geometry, then define two distinct source equations over that geometry—one quantum (electric charge), the other cosmic (gravitation).