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Geometry |
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Authors: Harish Chandra Rajpoot
In this work, the principal geometric parameters of the great rhombicuboctahedron, an Archimedean solid, are analytically derived. This polyhedron consists of 12 congruent square faces, 8 regular hexagonal faces, and 6 congruent regular octagonal faces of equal edge length, with 72 edges and 48 vertices lying on a circumscribed spherical surface. By applying HCR’s Theory of Polygon, explicit expressions are obtained for the solid angles subtended by each square, hexagonal, and octagonal face, as well as their corresponding normal distances from the center of the great rhombicuboctahedron. The formulation further yields the dihedral angles between adjacent faces, the inscribed radius, circumscribed radius, mean radius, surface area, and volume. The derived formulas are useful for the geometric analysis, design, and modeling of uniform (convex or non-convex) polyhedra.
Comments: 15 Pages. 5 Figures (Note by viXra Admin: An abstract in the article is required!)
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[v1] 2026-02-20 20:04:49
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