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Geometry |
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Authors: Harish Chandra Rajpoot
This paper presents a comprehensive tabulation of the solid angles subtended at the vertices of all thirteen Archimedean solids (convex uniform polyhedra). The solid angles are analytically evaluated using the standard solid angle formula in conjunction with tetrahedral decomposition. The resulting values constitute a consistent and complete set of reference data for the vertex geometry of the Archimedean solids, including the truncated tetrahedron, truncated hexahedron (cube), truncated octahedron, truncated dodecahedron, truncated icosahedron, cuboctahedron, icosidodecahedron, small rhombicuboctahedron, small rhombicosidodecahedron, snub cube, snub dodecahedron, great rhombicuboctahedron, and great rhombicosidodecahedron. These results provide useful quantitative tools for the geometric analysis and comparative study of uniform polyhedra.
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[v1] 2026-02-22 11:47:06
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