[[14,3,3]] Non-CSS Surface Code on a Rhombic Dodecahedron — E8 Intelligence Research

FINDING: A [[14,3,3]] non-CSS surface code is realized on the rhombic dodecahedron, a space-filling polyhedron with 14 vertices, 12 faces, and 24 edges, encoding 3 logical qubits with distance 3. | MATH: Code parameters: [[n=14, k=3, d=3]]. The rhombic dodecahedron has 14 vertices (data qubits), 12 faces (stabilizers, non-CSS), 24 edges (connectivity). The stabilizer group is non-CSS, meaning X- and Z-type stabilizers are not separable; instead, they are mixed Pauli operators. The code distance d=3 implies the minimum weight of a logical operator is 3. The polyhedron's symmetry group is the octahedral group (order 48), isomorphic to S₄ × C₂. | CONNECTION: The rhombic dodecahedron is the Voronoi cell of the face-centered cubic (FCC) lattice, a root lattice of type A₃ (or D₃). Its dual is the cuboctahedron, which has edge lengths in ratio 1:√2. The FCC lattice has packing density π/(3√2) ≈ 0.74048, and its reciprocal lattice is body-centered cubic (BCC). The rhombic dodecahedron's face a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com