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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

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n-dimensional polyhedron with special properties

I'd like to know if there exists a convex face transitive n-dimensional polyhedron with all dihedral angles equal to $\frac{2\pi}{3}$. For n = 2,3,4 an example can be a regular hexagon, a rhombic dode …
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