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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 dodecahedron and a 24-cell respectively. But I still got no idea what to do for n > 4.

Any help or ideas are appreciated, thank you!

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  • $\begingroup$ In four dimensions a second such polytope exists, which is the orthoplex/16-cell/dual of the hypercube. $\endgroup$
    – Oscar Lanzi
    Commented Jan 12 at 15:19

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