Über die Symmetriegruppen von regulärseitigen Polytopen. (On the symmetry groups of regular faced polytopes) (Q748894)

Convex polytopes are called regular faced, if all their facets are regular. It is known [\textit{N. W. Johnson}, Can. J. Math. 18, 169-200 (1966; Zbl 0132.146), \textit{V. A. Zalgaller}, Semin. Math. V. A. Steklov. Math. Inst., Leningrad (1969); translation from Zap. Nauk Semin. Leningrad. Otd. mat. Inst. Steklov 2, 1-221 (1967; Zbl 0165.563)] that all regular faced 3-polytopes have a nontrivial symmetry group. Here it is shown, that there exist regular faced d-polytopes with trivial symmetry group, but only for \(d=4\). The corresponding class of polytopes is studied.