Non-rational configurations, polytopes, and surfaces
نویسنده
چکیده
However, the dodecahedron and the icosahedron can be realized with rational coordinates if we do not require them to be precisely regular: If you perturb the vertices of a regular icosahedron “just a bit” into rational position, then taking the convex hull will yield a rational polytope that is combinatorially equivalent to the regular icosahedron. Similarly, by perturbing the facet planes of a regular dodecahedron a bit we obtain a dodecahedron with rational coordinates.
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