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Authors: Harish Chandra Rajpoot
In this paper, analytical formulas are derived using HCR’s Inverse Cosine Formula in conjunction with HCR’s Theory of Polygon. These formulas provide a simple and practical method for computing the internal (dihedral) angles between consecutive lateral faces of an arbitrary tetrahedron at any of its four vertices, as well as the solid angle subtended by the tetrahedron at a vertex when the apex angles between consecutive lateral edges meeting at that vertex are known. The resulting expressions are fully generalized and can also be applied to configurations in which three faces meet at a vertex of various regular and uniform polyhedra, enabling the calculation of the solid angle subtended by the polyhedron at that vertex.
Comments: 12 Pages, 3 Figures, Original Research
Download: PDF
[v1] 2026-02-22 11:54:14
Unique-IP document downloads: 85 times
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