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{"type":"standard","title":"Integral polytope","displaytitle":"Integral polytope","namespace":{"id":0,"text":""},"wikibase_item":"Q5166519","titles":{"canonical":"Integral_polytope","normalized":"Integral polytope","display":"Integral polytope"},"pageid":25293116,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_6.png/330px-Polyhedron_6.png","width":320,"height":320},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/e/e5/Polyhedron_6.png","width":4000,"height":4000},"lang":"en","dir":"ltr","revision":"1274658066","tid":"3d6c4483-e633-11ef-a646-93a812f34c41","timestamp":"2025-02-08T15:42:02Z","description":"A convex polytope whose vertices all have integer Cartesian coordinates","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Integral_polytope","revisions":"https://en.wikipedia.org/wiki/Integral_polytope?action=history","edit":"https://en.wikipedia.org/wiki/Integral_polytope?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Integral_polytope"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Integral_polytope","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Integral_polytope","edit":"https://en.m.wikipedia.org/wiki/Integral_polytope?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Integral_polytope"}},"extract":"In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex hull of its integer points.\nIntegral polytopes are also called lattice polytopes or Z-polytopes. The special cases of two- and three-dimensional integral polytopes may be called polygons or polyhedra instead of polytopes, respectively.","extract_html":"
In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex hull of its integer points.\nIntegral polytopes are also called lattice polytopes or Z-polytopes. The special cases of two- and three-dimensional integral polytopes may be called polygons or polyhedra instead of polytopes, respectively.
"}{"fact":"Cat paws act as tempetature regulators, shock absorbers, hunting and grooming tools, sensors, and more","length":102}
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