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Geometry |
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Authors: Harish Chandra Rajpoot
This paper presents an analytical derivation of the fundamental geometric parameters of a non-uniform tetradecahedron composed of two congruent regular hexagonal faces, twelve congruent trapezoidal faces, and eighteen vertices lying on a common circumscribed sphere. Using HCR’s Theory of Polygon, explicit closed-form expressions are obtained for the solid angles subtended at the center by the hexagonal and trapezoidal faces, as well as for the corresponding normal distances of these faces from the center. From these results, exact formulas for the inradius, circumradius, mean radius, total surface area, and enclosed volume of the polyhedron are systematically derived. The analytical framework developed herein provides a general and rigorous method for the geometric characterization of non-uniform polyhedra.
Comments: 11 Pages, 4 Figures
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[v1] 2026-02-22 11:49:33
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