Abstract
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
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Monson, B. (2013). Uniform Polyhedra from Diophantine Equations. In: Senechal, M. (eds) Shaping Space. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92714-5_19
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DOI: https://doi.org/10.1007/978-0-387-92714-5_19
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