Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming

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### Is the preimage of a face under an affine map a face?

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### Interpretation of this sum for concave bodies

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### Higher dimensional scutoids?

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### How rich is the class of vertex- and edge-transitive polytopes?

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### Complexity of 2D-Minkowski sum of non-convex polygons

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### Continuity of the combinatorial structure of a polytope with respect to face variables

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### Integral representations of finite groups and lattice point geometry

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### Conjecture on tilting modules for an Auslander algebra

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### Example of convex n-gon that cannot be decomposed into k congruent convex polygons

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### Realisation of a Polytope as a convex set [duplicate]

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### Probability that the perturbed convex hull is larger than the original one

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### On OR condition in Linear Programming with exponentially many constraints [closed]

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### Minimal combinatorial data needed to define a polytope [duplicate]

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### What separates a cyclic polytope from a projective polytope?

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### Why is the number of Hamiltonian Cycles of n-octahedron equivalent to the number of Perfect Matching in specific family of Graphs?

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### Refined f- and h-partition polynomials of the associahedra

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### Efficient $H$ representation of matrices with distinct cyclic shift permuted entries

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### How different can the constituents of an Ehrhart quasi-polynomial be?

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### Relative interior of a normal cone at a face of a convex polytope?

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### Size of a minimal non-negative conic basis

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### Parallelepiped is defined by the volumes of its faces

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### Triangulations of convex surfaces

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### Odds on rolling a rhombicosidodecahedron

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### Several convex polytopes in a simplex; fix an extreme point for each; how many can be supported by a function monotonic on all line segments?

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### Finding a point in the relative interior of the convex hull of a set of integer-valued vectors

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### Projecting two convex polyhedra onto their intersection

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### geometry of intersection of 2 polytope in higher dimension [closed]

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### Maximum number of integer points in a polytope

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### What is a natural way to extend a function from a subset of vertices to faces?

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### Reciprocity for multi-parameter Ehrhart polynomials

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### The “Johnson polychora”

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### Generalizations of 'Injectivity on one line'

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### Radial similarity of Newton polytopes

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### Bit complexity of Barvinok's algorithm

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### Minuscule weights of parabolic sub-root systems are not far from dominant

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### Quantitative error control in Minkowski-Stein formula

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### In convex optimization we know that the optimum solution is on which hyper plane

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### Factorization of tropical polynomials

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### 2-faces of reflexive Delzant polytopes

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### Who first used the word “Simplex”?

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### Product of two matrices of convex combinations [closed]

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### Influence of Vertex Weights on Performance of Polyhedral TSP Algorithms

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### Convex bodies have more volume on the outside near the boundary

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### Inequality on permutation polytope

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### How many ways can you inscribe five 24-cells in a 600-cell, hitting all its vertices?

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### Prove that the following set of triples forms a convex polytope

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### Counting lattice points can some give all?

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### intriguing Polytope

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### On necessary condition for polytopes with constant number or polynomial number of integer points?

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