edgeVerts

The module builds the smallest nontrivial multi-cube Freudenthal example: two unit cubes sharing one square face, each cut into six Freudenthal tetrahedra with matching face triangulation. Vertices are indexed by $V = \mathrm{Fin},12$ (eight corners of the first cube plus four new corners of the second). Edges are indexed by $E = \mathrm{Fin},33$.

The one-cube precursor lists nineteen unique edges on eight vertices. Gluing a second cube adds the new cube's internal edges and the four new outer face edges, while the five shared-face edges are not double-counted, yielding $19 + 19 - 5 = 33$.

This table is the concrete incidence data against which local edge slots inside each tetrahedron are matched after global deduplication.

Definition by exhaustive pattern match on the edge index. Cases $0$ through $32$ each return a fixed ordered pair $(i,j)$ of vertex indices. The residual constructor $\langle n+33, h\rangle$ is discharged by absurd plus omega, since no element of $\mathrm{Fin},33$ can satisfy that bound. No lemmas are invoked; the map is pure data.

Supplies the global edge list for the first multi-cube incidence instance beyond the single-cube sanity check. Downstream, edgeInTet_vertices and edgeInTet_iff_localEdgeOf use it to prove that every local tetrahedron edge slot lands on one of these thirty-three pairs (up to order). The same table is reused when the strip is viewed as a unit-step graph for rung-descent arguments in cosmology modules. In the broader Recognition geometry stack it is the concrete witness that Freudenthal face-matching survives cube-to-cube gluing, the step needed before any continuum or continuum-limit claim about the lattice.