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gptkbp:instanceOf
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gptkb:Polygon
Geometric object
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gptkbp:definedIn
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the convex hull of a finite set of points in Euclidean space
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gptkbp:dimensions
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n-dimensional
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gptkbp:example
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gptkb:dodecahedron
gptkb:icosahedron
gptkb:octahedron
gptkb:tetrahedron
gptkb:cross-polytope
cube
simplex
hypercube
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gptkbp:faced
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cells
ridges
edges
vertices
facets
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gptkbp:famous_result
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gptkb:Steinitz's_theorem
gptkb:Euler's_polyhedron_formula
gptkb:Minkowski–Weyl_theorem
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gptkbp:hasProperty
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bounded
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https://www.w3.org/2000/01/rdf-schema#label
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Convex polytopes
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gptkbp:namedFor
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gptkb:Euclid
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gptkbp:property
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bounded polyhedron
dual polytope exists
each face is itself a convex polytope
finite number of faces
intersection of finitely many half-spaces
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gptkbp:relatedConcept
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gptkb:Gale_diagram
gptkb:Euler's_formula
gptkb:Polygon
gptkb:Carathéodory's_theorem
gptkb:Minkowski_sum
gptkb:Farkas'_lemma
gptkb:Schlegel_diagram
convex hull
face lattice
H-representation
V-representation
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gptkbp:studiedBy
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combinatorics
optimization
convex geometry
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gptkbp:subclassOf
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gptkb:Polygon
gptkb:Convex_set
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gptkbp:used_in
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gptkb:geometry
operations research
mathematical optimization
linear programming
discrete geometry
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gptkbp:bfsParent
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gptkb:Polytopes
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gptkbp:bfsLayer
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7
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