Equipartite polytopes. (English) Zbl 1207.52013
The authors call a polytope equipartite if, for any partition of its vertex set into two equal-size sets \(V\) and \(W\), there is an isometry of the polytope that maps \(V\) onto \(W\). For every \(d\geq 2\), the main results read as follows: (1) an equipartite \(d\)-polytope has at most \(2d+2\) vertices and (2) there is an equipartite \(d\)-polytope with \(2d+2\) vertices. Besides, the authors construct several examples of equipartite \(d\)-polytopes and conjecture that the list is complete.
Reviewer: Victor Alexandrov (Novosibirsk)
MSC:
| 52B15 | Symmetry properties of polytopes |
| 52B11 | \(n\)-dimensional polytopes |
| 52B10 | Three-dimensional polytopes |
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