Truncated Dodecadodecahedron - Cartesian Coordinates

Cartesian Coordinates

Cartesian coordinates for the vertices of a truncated dodecadodecahedron are all the triples of numbers obtained by circular shifts and sign changes from the following points (where is the golden ratio):

$(1,1,3);\quad (\frac{1}{\varphi}, \frac{1}{\varphi^2}, 2\varphi);\quad (\varphi, \frac{2}{\varphi}, \varphi^2);\quad (\varphi^2, \frac{1}{\varphi^2}, 2);\quad (2\varphi-1,1,2\varphi-1).$

Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points.

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