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Geometry |
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Authors: Harish Chandra Rajpoot
In this paper, generalized analytical expressions are derived for determining the internal (dihedral) angles between consecutive faces of an arbitrary tetrahedron and the solid angle subtended at any of its vertices. The derivation is based on HCR’s Inverse Cosine Formula in conjunction with HCR’s Theory of Polygon. The resulting relations provide a simple and systematic method for evaluating the dihedral angles and the vertex solid angle when the three apex angles between the edges meeting at a given vertex are known. Owing to their general form, the derived formulae are also applicable to configurations in which three faces meet at a vertex of regular and uniform polyhedra, thereby enabling efficient computation of vertex solid angles in such solids.
Comments: 13 Pages. 5 Figures (Note by viXra Admin: An abstract labled as such is required in the article; further repetitions of similar articles may not be accepted)
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[v1] 2026-03-17 00:06:07
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