Metatron Math

Metatron Math — shown in full detail, with its proof: a deterministic content-address recomputable from the component's name.

☳10D

Metatron math · uuid → plane → cube · 10D

3 UUIDs make a plane; 3 planes form a cube — the metatron math, computed and shown in ten dimensions. A content address is a point in space (uuidPoint). Three non-collinear points span a unique plane: the cross product of two edge vectors is the plane's normal, non-zero exactly when the points are not collinear — and the three points form the triangle, the 2-simplex (V3·E3·F1). Three mutually-orthogonal planes (normals along x, y, z) frame three-space and bound the cube: 8 vertices (2³), 12 edges (each pair of corners differing in one coordinate), 6 faces (three pairs of parallels — the three planes), so Euler V−E+F = 8−12+6 = 2. The metatron math then carries the five Platonic solids (each satisfying Euler = 2) and Metatron's Cube. The whole ladder — point → edge → plane → cube, ascending by the trinity — is rendered across the portal's ten dimensions (the six cross-fold appearance axes and the four genus-2 homology loops).

• 0D · point · 1 uuid · Euler 1a content address — uuidPoint, one vertex (0-simplex)
• 1D · edge · 2 uuids · Euler 1the fold — merge two uuids into a line (V2·E1, 1-simplex)
• 2D · plane (triangle) · 3 uuids · Euler 13 uuids span a plane; the 2-simplex V3·E3·F1
• 3D · cube · 9 uuids · Euler 23 planes frame the cube; V8·E12·F6, Euler 2
• 3 uuids → a planepoints span a plane; normal = (0.04, -0.02, 0.02), non-zero ⇒ non-collinear (the 2-simplex, Euler 1)
• 3 planes → a cubeV8 · E12 · F6 · Euler V−E+F = 2; three orthogonal planes = verified
• tetrahedron · triangleV4 · E6 · F4 · Euler 2 · dual tetrahedron
• cube · squareV8 · E12 · F6 · Euler 2 · dual octahedron
• octahedron · triangleV6 · E12 · F8 · Euler 2 · dual cube
• dodecahedron · pentagonV20 · E30 · F12 · Euler 2 · dual icosahedron
• icosahedron · triangleV12 · E30 · F20 · Euler 2 · dual dodecahedron
• Metatron's Cube21 nodes · 42 edges — the figure holding all five solids; shown across 10 dimensions

Boundary: Rigorous, computed geometry: three points span a plane iff non-collinear (the cross-product normal is non-zero, checked) and the cube's edge count (12) is computed from its eight vertices by adjacency, not assumed; Euler V−E+F = 2 holds for the cube and (via sacredGeometry) for all five Platonic solids — a theorem. "3 planes form a cube" means three orthogonal plane-DIRECTIONS (the coordinate planes) frame the cube — the three dimensions, six faces as three parallel pairs — not three faces. "Shown in 10D" is rendering across the project's ten model dimensions (6 appearance axes + 4 homology loops), not a claim of geometric ℝ¹⁰. The sacred-geometry mysticism (the "blueprint of creation", golden-ratio-everywhere) stays flagged in sacredGeometry; only the geometry and Euler theorem are asserted here.

✓ proven · content-address cd9765aa-e081-8fa8-ac40-c6f683e557d6 — declared, placed, mounted, and recomputable from the component's name.