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The Circumsphere of a Cubic Hyperpyramid: Tesseract and √7-Symmetry Connection

Author:

Turanyanin, Dragan N.

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

December 27, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10423

Downloads:

Keywords:

N/A

Abstract:

We derive the exact formula for the circumsphere (hypersphere) of a cubic hyperpyramid in 4D Euclidean space. A cubic hyperpyramid consists of a cubic base in a 3D hyperplane and an apex point elevated in the fourth dimension. For a base cube with edge length k and apex height H, we establish that the circumsphere has radius R = (4H² + 3k²)/(8H) with center positioned at height c = (4H² – 3k²)/(8H) along the symmetry axis. Connection with 4-cube (tesseract) and a √7 based symmetry surprisingly emerge.

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