Journal for Geometry and Graphics 29 (2025), No. 2, 139--148
Copyright by the authors licensed under CC BY SA 4.0
Extension of the Formula for the Sum of Fourth Powers of Distances in Regular Polytopes
Tran Quang Hung
High School for Gifted Students, Vietnam National University, Hanoi, Vietnam
tranquanghung@hus.edu.vn
We extend distance–power identities for regular figures by deriving formulas for the sum of fourth powers of distances from an arbitrary point to the vertices of regular polygons and polyhedra. The method employs embeddings of these configurations into higher–dimensional Euclidean spaces and systematic use of the Pythagorean theorem. Our results unify and generalize known formulas in lower dimensions, providing a broader framework for distance relations in regular polytopes.
Keywords: Regular polytope, regular polygon, Pythagorean theorem, fourth powers of distances.
MSC: 51M04; 51N20.
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