The Honeycomb Unit as a Simplicial Complex and Its Local Curvature

Paper 1 of an 8 part series. This paper introduces the Honeycomb Unit (HU) as the fundamental simplicial building block of the Honeyverse, modeling space as a discrete tetrahedral–octahedral lattice whose geometric behavior emerges from combinatorial structure rather than continuous fields. The HU is treated as a 3‑dimensional simplicial complex composed of vertices, edges, triangular faces, and tetrahedra, each contributing to local curvature through deficit angles around edges. By analyzing how these units assemble and how their angular mismatches accumulate, the paper establishes a metric‑like curvature mechanism grounded entirely in discrete adjacency relations. This work provides the foundational geometric substrate for the broader Honeyverse framework developed across the eight‑paper series. The HU lattice supplies the “inward‑binding” component of the theory, generating local curvature, structure formation, and early‑epoch gravitational behavior. Its interaction with the outward‑expanding ghost dual complex explored in later papers forms the core duality of the Honeyverse: a universe shaped jointly by metric primal geometry and combinatorial negative‑space structure. This paper establishes the mathematical groundwork upon which the remaining Honeyverse papers build. v1