A convex polytope whose vertices all have integer Cartesian coordinates
Cube
Cuboctahedron
Octahedron
Truncated octahedron
(±1, ±1, ±1)
(0, ±1, ±1)
(0, 0, ±1)
(0, ±1, ±2)
Four integral polytopes in three dimensions
In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates.[1] That is, it is a polytope that equals the convex hull of its integer points.[2]
Integral 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.
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combinatorics, an integralpolytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the...
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