A polyhedron of genus 4 with minimal number of vertices and maximal symmetry
The minimal number of vertices v(g) of a triangulation of the orientable 2-manifold of genus g is known [\textit{M. Jungerman} and \textit{G. Ringel}, Acta Math. 145, 121-154 (1980; Zbl 0451.57005)]. In \textit{L. Szilassi}, Topologie Struct. 13, 69-80 (1986; Zbl 0605.52002) and the second author's paper in Mathematika 34, No.2, 237-242 (1987; Zbl 0633.52005) for \(g=1,2,3\) it is shown that for the minimal number V(g) of vertices of a polyhedron of genus g, \(V(g)=v(g)\) holds. In the present paper \(V(4)=v(4)=11\) is proved. Moreover, the extremal polyhedron admits maximal symmetry.
scientific article; zbMATH DE number 4101991