Five known combinatorial regular polyhedra with genus g ≥ 2 and with the rotation group of a Platonic solid are described, along with their history. They are close (hyperbolic) analogues of the Platonic solids. The protagonists of their discovery are Leonardo da Vinci and two mathematicians: Alicia Boole Stott and Harold Scott MacDonald Coxeter. For a sixth candidate we discovered that there is so far only a Kepler-Poinsot type available. This is a correction of a result from 1986.
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Bokowski et al. (2022) studied this question.
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