Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 1, pp. 97-106 (2008)

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Combinatorial $3$-manifolds with $10$ vertices

Frank H. Lutz

Technische Universität Berlin, Fakultät II -- Mathematik und Naturwissenschaften, Institut für Mathematik, Sekretariat MA 3-2, Straße des 17. Juni 136, 10623 Berlin, Germany, e-mail:

Abstract: We give a complete enumeration of all combinatorial $3$-manifolds with $10$ vertices: There are precisely $247882$ triangulated $3$-spheres with $10$ vertices as well as $518$ vertex-minimal triangulations of the sphere product $S^2\times S^1$ and $615$ triangulations of the twisted sphere product $S^2\hbox{$\times \hspace{-1.62ex}_\hspace{-.4ex}_\hspace{.7ex}$}S^1$. All the $3$-spheres with up to $10$ vertices are shellable, but there are $29$ vertex-minimal non-shellable $3$-balls with $9$ vertices.

Editorial remark: Due to a mixup, the Table 3 in the first published electronical version of the paper in this volume is not the version the author wanted to submit to the journal. The obsoleted version is kept at 5v1.html. The current version represents now the same version as the printed article in this journal.}

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Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.

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