Shaping Space pp 253-255 | Cite as

Uniform Polyhedra from Diophantine Equations

  • Barry MonsonEmail author


A simple set of coordinates eases the study of metrical properties of uniform polyhedra. For instance, the six vertices of the regular octahedron {3,4} have Cartesian coordinates (±1,0,0), etc. where “etc.” means “permute the coordinates in all possible ways.” I find it pleasing in such examples that the coordinates are given by systematic choices. Observe further that the coordinates provide all integral solutions to the Diophantine equation


Integral Solution Diophantine Equation Golden Ratio Algebraic Integer Metrical Property 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New BrunswickFrederictonCanada

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