• Mathematics
  • Published 2002

The edge-minimal polyhedral maps of Euler characteristic - 8

@inproceedings{Brehm2002TheEP,
  title={The edge-minimal polyhedral maps of Euler characteristic - 8},
  author={Ulrich Brehm and Basudeb Datta and Nandini Nilakantan},
  year={2002}
}
In [B], a $\{5, 5\}$-equivelar polyhedral map of Euler characteristic $-8$ was constructed. In this article we prove that $\{5, 5\}$-equivelar polyhedral map of Euler characteristic $-8$ is unique. As a consequence, we get that the minimum number of edges in a non-orientable polyhedral map of Euler characteristic $-8$ is $ > 40$. We have also constructed $\{5, 5\}$-equivelar polyhedral map of Euler characteristic $-2m$ for each $m ≥ 4$. 

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