Self-Healing Network Topologies: From Platonic Solids to Egyptian Grammar

I identify a sequence of self-healing network sizes emerging from two interleaved derivation chains: a geometric chain rooted in Platonic solids (12 → 60 → 120) and an algebraic chain derived from Egyptian phonemic architecture (136 → 240 → 408). The chains intersect at T(15) = 120, the vertex count of the 4D 600-cell. All eight candidate sizes (12, 36, 60, 80, 120, 136, 240, 408) are experimentally confirmed to maintain connectivity under arbitrary single-node removal.