feat: add Platonic classification eval problem#302
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§42 of Knill's "Some Fundamental Theorems in Mathematics". The count p_d of regular convex d-polytopes up to similarity is (∞, 5, 6, 3, 3, …): ∞ in dim 2, 5 in dim 3 (Euclid XIII), 6 in dim 4 (Schläfli 1850s), 3 in every dim ≥ 5. Mathlib has the supporting convex-geometry machinery but no convex-polytope datatype, face lattice, regular-polytope concept, or classification counts. The Challenge ships ~1.5 pages of helper defs. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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§42 of Knill's "Some Fundamental Theorems in Mathematics". Schläfli's 1852 dimension-by-dimension enumeration of the regular convex polytopes: p_3 = 5 (Euclid XIII — the five Platonic solids), p_4 = 6 (Schläfli's six regular 4-polytopes), and p_d = 3 for every d ≥ 5 (regular simplex, hypercube, cross-polytope). Companion to the broader Platonic classification problem #302, which additionally records p_2 = ∞. Mathlib has convex-geometry primitives but no convex-polytope datatype, face lattice, regular-polytope concept, or classification counts; the Challenge ships ~1.5 pages of helper defs. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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§42 of Knill's "Some Fundamental Theorems in Mathematics". Schläfli's 1852 dimension-by-dimension enumeration of the regular convex polytopes: p_3 = 5 (Euclid XIII — the five Platonic solids), p_4 = 6 (Schläfli's six regular 4-polytopes), and p_d = 3 for every d ≥ 5 (regular simplex, hypercube, cross-polytope). Companion to the broader Platonic classification problem #302, which additionally records p_2 = ∞. Mathlib has convex-geometry primitives but no convex-polytope datatype, face lattice, regular-polytope concept, or classification counts; the Challenge ships ~1.5 pages of helper defs. Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
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This PR adds the Platonic classification as a new lean-eval challenge problem — §42 of Oliver Knill's Some Fundamental Theorems in Mathematics.
The count
p_dof regular convexd-polytopes (Platonic polytopes) up to similarity is:p_2 = ∞— regular polygons (one for eachn ≥ 3)p_3 = 5— Euclid XIII (tetrahedron, cube, octahedron, dodecahedron, icosahedron)p_4 = 6— Schläfli 1850s (5-cell, 8-cell, 16-cell, 24-cell, 120-cell, 600-cell)p_d = 3for everyd ≥ 5— regular simplex, hypercube, cross-polytopemathlib has
convexHull,extremePoints,IsExposed,vectorSpan,AffineIsometryEquiv, andSet.encard— but no convex-polytope datatype, no face lattice, no regular-polytope concept, and none of the classification counts. The Challenge ships ~1.5 pages of definitions (ConvexPolytope,dim,IsFace,Flag,isSymmetry,IsRegular,Similar,regularPolytopes,regularSimilar,platonicCount).🤖 Prepared with Claude Code