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

Kyongil Yoon
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 509–512 Short Papers


There are five Platonic solids and thirteen Archimedean solids, and they have many interesting characteristics. One of them is that their faces can be projected outward to a circumscribing sphere, producing tilings of the sphere. In this paper we show how to use analytical methods to calculate the lengths of the geodesics and the measures of the angles for these tilings.