Semi-equivelar maps (Q2452342)

A semi-equivelar map (SEM) of type \((3^p, 4^q)\) is a polyhedral map on a surface in which each vertex is in \(p\) triangles and in \(q\) quadrangles. The authors show that there exist exactly three SEMs of type \((3^5, 4^1)\) on the surface of Euler characteristic \(-1\). The authors also present examples of (i) SEMs of type \((3^5, 4^1)\) on orientable and non-orientable surfaces of Euler characteristic \(-2\), (ii) SEMs of type \((3^5, 4^2)\) on orientable and non-orientable surfaces of Euler characteristic \(-8\), and (iii) SEMs of type \((3^7, 4^1)\) on orientable and non-orientable surfaces of Euler characteristic \(-10\).