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== Symmetries == A duoprism made out of polytopes ''P'' and ''Q'' with symmetry groups ''G'' and ''H'' will, most of the time, have a [[symmetry group]] equal to the [[direct product]] ''G'' × ''H''. There's some exceptions to this rule, however. If ''P'' and ''Q'' are congruent, there will also be a symmetry swapping the bases, making the symmetry group at least the [[wreath product]] ''G'' ≀ S<sub>2</sub>. In other exceptional cases, the symmetry group might be even larger, as is the case with prism products of [[hypercube]]s.
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