Realizations of regular toroidal maps of type \(\{4,4\}\)
In [Aequationes Math. 37, No. 1, 38-56 (1989; Zbl 0676.51008)], the reviewer introduced a general theory of Euclidean realizations of abstract regular polytopes. In this paper, the authors describe the realization spaces of the regular toroidal polyhedra \(\{4, 4\}_{(b,c)}\), with \(b\geq c\) and \(bc(b-c)=0\). When \(b\geq 2\), the number of non-trivial pure realizations of \(\{4,4\}_{(b,0)}\) is \(r={1\over 2}\lfloor b/2 \rfloor (\lfloor b/2\rfloor +3)\), and when \(c\geq 2\), the number of non-trivial pure realizations of \(\{4,4\}_{(c,c)}\) is \(r'=c+\lfloor c^2/4\rfloor\).
scientific article; zbMATH DE number 1507688