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MSC2020 · 52Bxx

Polytopes and polyhedra

Polytopes and polyhedra

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Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

52B05Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)1 52B10Three-dimensional polytopes0 52B11

n

-dimensional polytopes0 52B12Special polytopes (linear programming, centrally symmetric, etc.)0 52B15Symmetry properties of polytopes0 52B20Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)0 52B22Shellability for polytopes and polyhedra0 52B35Gale and other diagrams0 52B40Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)0 52B45Dissections and valuations (Hilbert's third problem, etc.)0 52B55Computational aspects related to convexity0 52B60Isoperimetric problems for polytopes0 52B70Polyhedral manifolds0 52B99Polytopes and polyhedra0

Mapped problems

OP-11963Geometry and topologyOpen

The Hirsch Conjecture in Dimension 4

The Hirsch Conjecture in Dimension 4. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

Journals & articles in MSC 52

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Discrete & Computational Geometry ↗

Springer Nature

Discrete geometry and geometric computation

The crystallization conjecture: a review
2015 · 1 questions extracted

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MSC2020 © Mathematical Reviews (AMS) and zbMATH · CC BY-NC-SA 4.0 · Official PDF, page 138