Geometry

   

Dihedral Angles Between the Polygonal Faces in Various Regular & Uniform Polyhedra: Platonic and Archimedean Solids

Authors: Harish Chandra Rajpoot

This paper presents a set of practically oriented analytical formulas and tables compiled from geometric data of various convex uniform polyhedra, listing the dihedral angles between two faces with or without sharing a common edge. These formulas and tables are specifically intended to support the physical and computational construction of convex uniform polyhedral shells composed of different regular polygonal faces. By using the tabulated dihedral angles, wire-frame and shell models of polyhedra can be constructed efficiently by successively joining adjacent planar faces at their common edges with the correct angular orientation. The presented data are particularly useful for applications in geometric modeling, structural design, educational model fabrication, and the development of computational algorithms for polyhedral assembly. Overall, the tables provide a convenient and reliable reference for the practical realization and analysis of convex uniform polyhedral structures.

Comments: 29 Pages, 8 Figures, Original Research

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Submission history

[v1] 2026-02-03 11:26:38

Unique-IP document downloads: 165 times

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