Analytical Calculation of Geodesic Lengths and Angle Measures on Sphere Tiling of Platonic and Archimedean Solids

Year: 2012 Authors: Kyongil Yoon

Core claim

All eighteen Platonic and Archimedean solids admit analytically computed geodesic lengths and spherical polygon angles on their circumscribed-sphere tilings.

Topics

spherical tilings, geodesic length, interior angle measures, Platonic solids, Archimedean solids

Domains

spherical trigonometry, polyhedra, geodesic geometry, cubic equations, modular origami, architecture, geometric design, polyhedral art

Methods

analytical calculation, law of cosines, Napier’s rules, cubic formula

Media

sphere, great-circle arcs, spherical polygons, polyhedral models

Source status

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