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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
11
votes
polyhedra with equilateral pentagons faces
The pentagonal isohedra with sides of equal length listed on http://loki3.com/poly/isohedra.html are the regular dodecahedron, non-convex equilateral pyritohedron, equilateral pentagonal icositetrahed …
9
votes
Fair but irregular polyhedral dice
Yes, there are conditions broader than isohedral symmetry that guarantee a convex polyhedron represents a fair die. Consider a teetotum or dreidl. These shapes aren't isohedra, but they are mathemat …