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The center of a polytope is the point that is taken to be in its middle. They can be defined in several ways. Centers are generally assumed to be preserved by reflection, rotation and scaling.

By averages of points[edit | edit source]

By inscription and circumscription[edit | edit source]

By symmetry[edit | edit source]

For any definition of center that is preserved by rotation, reflection and scaling, the center of a polytope must be preserved by the polytope's symmetries. If there is only one point that is preserved by a polytope's symmetries (as in all isogonal polytopes), that point is the polytope's center.