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Geometry |
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Authors: Harish Chandra Rajpoot
In this paper, the principal geometric parameters of the great rhombicosidodecahedron, the largest Archimedean solid, are analytically derived. This polyhedron consists of 30 congruent square faces, 20 regular hexagonal faces, and 12 congruent regular decagonal faces, all of equal edge length, with 180 edges and 120 vertices lying on a circumscribed sphere. By applying HCR’s Theory of Polygon, explicit expressions are obtained for the solid angles subtended by each square, hexagonal, and decagonal face, along with their corresponding normal distances from the center of the great rhombicosidodecahedron. The derived formulation further yields the dihedral angles between adjacent faces, the inscribed radius, circumscribed radius, mean radius, surface area, and volume. The resulting formulas are useful for the geometric analysis, design, and modeling of uniform polyhedra.
Comments: 16 Pages. 5 Figures (Note by viXra Admin: An abstract in the article is required!)
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[v1] 2026-02-20 20:04:30
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