%I
%S 1,2,4,6,8,14,18,23,38,47,58,79,118,128,159
%N Number of rigid genus2 bipartite crystallizations of orientable 3manifolds with 2n vertices.
%C This is the upper row of Table 1, p.9, of Bandieri, et al. There are no rigid genus two crystallizations with less than 14 vertices (i.e., with n = 7). Abstract: "We improve and extend to the nonorientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra." Karabas, Malicki and Nedela show that there exist exactly 78 nonhomeomorphic, closed, orientable, prime 3manifolds with Heegaard genus two, admitting a colored triangulation with at most 42 tetrahedra. Each manifold M is identified by a suitable 6tuple of nonnegative integers, representing a minimal crystallization  hence a minimal colored triangulation  of M. From such a 6tuple, a presentation of the fundamental group and of the first homology group of M are easily obtained.
%D P. Bandieri et al., A census of genustwo 3manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 24692481.
%H Paola Bandieri, Paola Cristofori and Carlo Gagliardi, <a href="http://arxiv.org/abs/0902.0492">A census of genus two 3manifolds up to 42 coloured tetrahedra</a>, Feb 3, 2009.
%H J. Karabas, P. Malicky, R. Nedela, <a href="http://dx.doi.org/10.1016/j.disc.2006.11.017">Threemanifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices</a>, Discrete Math. 307 (2007), no. 21, 25692590.
%Y Cf. A156098.
%K nonn,more
%O 7,2
%A _Jonathan Vos Post_, Feb 04 2009
%E Edited by _N. J. A. Sloane_, Sep 26 2010
