feat: add Schläfli classification eval problem#303
Open
kim-em wants to merge 1 commit into
Open
Conversation
§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>
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This PR adds an eval problem for Schläfli's classification of the regular
convex polytopes:
p_3 = 5(Euclid XIII — the five Platonic solids),p_4 = 6(Schläfli's six regular 4-polytopes), andp_d = 3for everyd ≥ 5(regular simplex, hypercube, cross-polytope). §42 of Knill'sSome Fundamental Theorems in Mathematics. Companion to the broader
Platonic classification problem (#302), which additionally records the
p_2 = ∞case.Mathlib has
convexHull,extremePoints,IsExposed,vectorSpan,AffineIsometryEquiv, andSet.encard, but no convex-polytope datatype,face lattice, regular-polytope concept, or classification counts. The
Challenge ships ~1.5 pages of helper defs (
ConvexPolytope,dim,IsFace,Flag,isSymmetry,IsRegular,Similar,regularPolytopes,regularSimilar,platonicCount).No formalization in any major prover. Not on Freek Wiedijk's 100-theorems
list.
🤖 Prepared with Claude Code