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May 9, 2020 at 18:59 comment added M. Winter @HarryRichman I see, that was unexpected. In my application I have additional assumptions on the polytope, namely, that its $(d-2)$-faces are simplices, so I suppose this is an essential assumption. Anyway, I will need to think about this and maybe edit the question.
May 9, 2020 at 18:57 history edited M. Winter CC BY-SA 4.0
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May 9, 2020 at 18:54 comment added Harry Richman As stated I think the answer is yes for all $d$: just take the cube and "squash" it slightly so some dihedral angles increase and some decrease.
May 9, 2020 at 18:51 comment added Harry Richman For reference when $d=3$: en.wikipedia.org/wiki/Table_of_polyhedron_dihedral_angles. Is the answer known for small $d$?
May 9, 2020 at 17:47 history edited M. Winter CC BY-SA 4.0
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May 9, 2020 at 17:39 history edited M. Winter CC BY-SA 4.0
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May 9, 2020 at 17:29 history asked M. Winter CC BY-SA 4.0