\begin{thebibliography}{DHSW04}

\bibitem[BAB12]{regina}
William Pettersson et~al. Benjamin A.~Burton, Ryan~Budney.
\newblock Regina: Software for 3-manifold topology and normal surface theory,
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\newblock {\tt http://\allowbreak regina.\allowbreak sourceforge.\allowbreak
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\bibitem[Ban65]{Banchoff65TightEmb3DimPolyMnf}
Thomas~F. Banchoff.
\newblock {T}ightly embedded {$2$}-dimensional polyhedral manifolds.
\newblock {\em Amer. J. Math.}, 87:462--472, 1965.

\bibitem[Ban74]{Banchoff74TightPolyKBProjPMB}
Thomas~F. Banchoff.
\newblock {T}ight polyhedral {K}lein bottles, projective planes, and {M}\"obius
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\newblock {\em Math. Ann.}, 207:233--243, 1974.

\bibitem[BD08a]{Bagchi08LBTNormPseudoMnf}
Bhaskar Bagchi and Basudeb Datta.
\newblock {L}ower bound theorem for normal pseudomanifolds.
\newblock {\em Expo. Math.}, 26(4):327--351, 2008.

\bibitem[BD08b]{Bagchi08OnWalkupKd}
Bhaskar Bagchi and Basudeb Datta.
\newblock {O}n {W}alkup's class $\mathcal{K}(d)$ and a minimal triangulation of
  a 4-manifold.
\newblock {\tt arXiv:0804.2153v1 [math.GT]}, Preprint, 8 pages, 2008.

\bibitem[BK97]{Banchoff97TightSubmSmoothPoly}
Thomas~F. Banchoff and Wolfgang K{\"u}hnel.
\newblock {T}ight submanifolds, smooth and polyhedral.
\newblock In {\em Tight and taut submanifolds ({B}erkeley, {CA}, 1994)},
  volume~32 of {\em Math. Sci. Res. Inst. Publ.}, pages 51--118. Cambridge
  Univ. Press, Cambridge, 1997.

\bibitem[BK08]{Brehm08EquivMapsTorus}
Ulrich Brehm and Wolfgang K{\"u}hnel.
\newblock {E}quivelar maps on the torus.
\newblock {\em European J. Combin.}, 29(8):1843--1861, 2008.

\bibitem[BK09]{Brehm09LatticeTrigE33Torus}
U.~Brehm and W.~K\"uhnel.
\newblock Lattice triangulations of {$E^3$} and of the $3$-torus, 2009.
\newblock {To appear in Israel J. Math.}

\bibitem[BL98]{Breuer98GAP4TypeSystem}
Thomas Breuer and Steve Linton.
\newblock The gap 4 type system: organising algebraic algorithms.
\newblock In {\em Proceedings of the 1998 international symposium on Symbolic
  and algebraic computation}, ISSAC '98, pages 38--45, New York, NY, USA, 1998.
  ACM.

\bibitem[BL00]{Bjoerner00SimplMnfBistellarFlips}
Anders Bj{\"o}rner and Frank~H. Lutz.
\newblock {S}implicial manifolds, bistellar flips and a 16-vertex triangulation
  of the {P}oincar{\'e} homology 3-sphere.
\newblock {\em Experiment. Math.}, 9(2):275--289, 2000.

\bibitem[BR08]{HomAlg}
Mohamed Barakat and Daniel Robertz.
\newblock {\tt homalg}: a meta-package for homological algebra.
\newblock {\em J. Algebra Appl.}, 7(3):299--317, 2008.

\bibitem[CK01]{Casella01TrigK3MinNumVert}
Mario Casella and Wolfgang K{\"u}hnel.
\newblock {A} triangulated {$K3$} surface with the minimum number of vertices.
\newblock {\em Topology}, 40(4):753--772, 2001.

\bibitem[Con09]{Conder09RegMapsOfBdChi}
Marston D.~E. Conder.
\newblock Regular maps and hypermaps of {E}uler characteristic {$-1$} to
  {$-200$}.
\newblock {\em J. Combin. Theory Ser. B}, 99(2):455--459, 2009.

\bibitem[Dat07]{Datta07MinTrigManifolds}
Basudeb Datta.
\newblock {M}inimal triangulations of manifolds.
\newblock {\em J. Indian Inst. Sci.}, 87(4):429--449, 2007.

\bibitem[DHSW04]{Dumas04Homology}
J.-G. Dumas, F.~Heckenbach, B.~D. Saunders, and V.~Welker.
\newblock {S}implicial {H}omology, v. 1.4.2.
\newblock {\url{http://www.cis.udel.edu/~dumas/Homology/}}, 2004.

\bibitem[DKT08]{Desbrun08DiscDiffFormCompModel}
Mathieu Desbrun, Eva Kanso, and Yiying Tong.
\newblock {D}iscrete differential forms for computational modeling.
\newblock In {\em Discrete differential geometry}, volume~38 of {\em
  Oberwolfach Semin.}, pages 287--324. Birkh\"auser, Basel, 2008.

\bibitem[Eff11a]{Effenberger10Diss}
Felix Effenberger.
\newblock {\em {H}amiltonian submanifolds of regular polytopes}.
\newblock Logos Verlag, Berlin, 2011.
\newblock Dissertation, University of Stuttgart, 2010.

\bibitem[Eff11b]{Effenberger09StackPolyTightTrigMnf}
Felix Effenberger.
\newblock {S}tacked polytopes and tight triangulations of manifolds.
\newblock {\em Journal of Combinatorial Theory, Series A}, 118(6):1843 -- 1862,
  2011.

\bibitem[For95]{Forman95DiscrMorseTheoryCellCompl}
Robin Forman.
\newblock A discrete {M}orse theory for cell complexes.
\newblock In {\em Geometry, topology, \& physics}, Conf. Proc. Lecture Notes
  Geom. Topology, IV, pages 112--125. Int. Press, Cambridge, MA, 1995.

\bibitem[Fro08]{Frohmader08FaceVecFlagCompl}
Andrew Frohmader.
\newblock Face vectors of flag complexes.
\newblock {\em Israel J. Math.}, 164:153--164, 2008.

\bibitem[GJ00]{Joswig00Polymake}
Ewgenij Gawrilow and Michael Joswig.
\newblock polymake: a framework for analyzing convex polytopes.
\newblock In {\em Polytopes---combinatorics and computation (Oberwolfach,
  1997)}, volume~29 of {\em DMV Sem.}, pages 43--73. Birkh{\"a}user, Basel,
  2000.

\bibitem[Gr{\"u}03]{Gruenbaum03ConvPoly}
Branko Gr{\"u}nbaum.
\newblock {\em {C}onvex polytopes}, volume 221 of {\em Graduate Texts in
  Mathematics}.
\newblock Springer-Verlag, New York, second edition, 2003.
\newblock Prepared and with a preface by Volker Kaibel, Victor Klee and
  G{\"u}nter M.\ Ziegler.

\bibitem[GS09]{M2}
Daniel~R. Grayson and Michael~E. Stillman.
\newblock {M}acaulay2, a software system for research in algebraic geometry,
  {V}ersion 1.3.1.
\newblock \url{http://www.math.uiuc.edu/Macaulay2/}, 2009.

\bibitem[Hak61]{Haken61TheoNormFl}
Wolfgang Haken.
\newblock {T}heorie der {N}ormalfl{\"a}chen.
\newblock {\em Acta Math.}, 105:245--375, 1961.

\bibitem[Hau00]{Hauser2000}
Herwig Hauser.
\newblock Resolution of singularities 1860--1999.
\newblock In {\em Resolution of singularities ({O}bergurgl, 1997)}, volume 181
  of {\em Progr. Math.}, pages 5--36. Birkh\"auser, Basel, 2000.

\bibitem[Hir53]{Hirzebruch1953}
Friedrich E.~P. Hirzebruch.
\newblock \"uber vierdimensionale riemannsche fl\"achen mehrdeutiger
  analyti\-scher funktionen von zwei komplexen ver\"anderlichen.
\newblock {\em Math. Ann.}, 126:1 -- 22, 1953.

\bibitem[Hop51]{Hopf1951}
Heinz Hopf.
\newblock \"{U}ber komplex-analytische {M}annigfaltigkeiten.
\newblock {\em Univ. Roma. Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5)},
  10:169--182, 1951.

\bibitem[Hud69]{Hudson69PLTop}
John F.~P. Hudson.
\newblock {\em {P}iecewise linear topology}.
\newblock University of Chicago Lecture Notes prepared with the assistance of
  J. L. Shaneson and J. Lees. W. A. Benjamin, Inc., New York-Amsterdam, 1969.

\bibitem[Hup67]{Huppert67EndlGruppen}
Bertram Huppert.
\newblock {\em Endliche {G}ruppen. {I}}.
\newblock Die Grundlehren der Mathematischen Wissenschaften, Band 134.
  Springer-Verlag, Berlin, 1967.

\bibitem[KL99]{Kuehnel99CensusTight}
Wolfgang K{\"u}hnel and Frank~H. Lutz.
\newblock {A} census of tight triangulations.
\newblock {\em Period. Math. Hungar.}, 39(1-3):161--183, 1999.
\newblock {D}iscrete geometry and rigidity ({B}udapest, 1999).

\bibitem[KN11]{Klee11CentSymmMnfFewVert}
Steven Klee and Isabella Novik.
\newblock {C}entrally symmetric manifolds with few vertices.
\newblock {\tt arXiv:1102.0542v1 [math.CO]}, Preprint, 15 pages, 2011.

\bibitem[Kne29]{Kneser29ClosedSurfIn3Mflds}
Hellmuth Kneser.
\newblock {Geschlossene Fl\"{a}chen in dreidimensionalen Mannigfaltigkeiten}.
\newblock {\em Jahresbericht der deutschen Mathematiker-Vereinigung},
  38:248--260, 1929.

\bibitem[K{\"u}h86]{Kuehnel86HigherDimCsaszar}
Wolfgang K{\"u}hnel.
\newblock {H}igher dimensional analogues of {C}s{\'a}sz{\'a}r's torus.
\newblock {\em Results Math.}, 9:95--106, 1986.

\bibitem[K{\"u}h94]{Kuehnel94ManSkelConvPolyt}
Wolfgang K{\"u}hnel.
\newblock {M}anifolds in the skeletons of convex polytopes, tightness, and
  generalized {H}eawood inequalities.
\newblock In {\em Polytopes: abstract, convex and computational (Scarborough,
  ON, 1993)}, volume 440 of {\em NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
  pages 241--247. Kluwer Acad. Publ., Dordrecht, 1994.

\bibitem[K{\"u}h95]{Kuehnel95TightPolySubm}
Wolfgang K{\"u}hnel.
\newblock {\em {T}ight polyhedral submanifolds and tight triangulations},
  volume 1612 of {\em Lecture Notes in Mathematics}.
\newblock Springer-Verlag, Berlin, 1995.

\bibitem[Kui84]{Kuiper84GeomTotAbsCurvTheo}
Nicolaas~H. Kuiper.
\newblock {G}eometry in total absolute curvature theory.
\newblock In {\em Perspectives in mathematics}, pages 377--392. Birkh{\"a}user,
  Basel, 1984.

\bibitem[Lut]{Lutz08ManifoldPage}
Frank~H. Lutz.
\newblock {T}he {M}anifold {P}age.
\newblock {\url{http://www.math.tu-berlin.de/diskregeom/stellar}}.

\bibitem[Lut03]{Lutz03TrigMnfFewVertVertTrans}
Frank~H. Lutz.
\newblock {\em {T}riangulated {M}anifolds with {F}ew {V}ertices and
  {V}ertex-{T}ransitive {G}roup {A}ctions}.
\newblock PhD thesis, TU Berlin, 2003.

\bibitem[Lut05]{Lutz05TrigMnfFewVertCombMnf}
Frank~H. Lutz.
\newblock {T}riangulated {M}anifolds with {F}ew {V}ertices: {C}ombinatorial
  {M}anifolds.
\newblock {\tt arXiv:math/0506372v1 [math.CO]}, Preprint, 37 pages, 2005.

\bibitem[McK84]{McKay84Nauty}
Brendan McKay.
\newblock The nauty page.
\newblock {\url{http://cs.anu.edu.au/people/bdm/nauty/}}, 1984.

\bibitem[Pac87]{Pachner87KonstrMethKombHomeo}
Udo Pachner.
\newblock {K}onstruktionsmethoden und das kombinatorische
  {H}om\"{o}omorphieproblem f\"{u}r {T}riangulierungen kompakter semilinearer
  {M}annigfaltigkeiten.
\newblock {\em Abh. Math. Sem. Uni. Hamburg}, 57:69--86, 1987.

\bibitem[R\"07]{Roeder07Polymaking}
Marc R\"{o}der.
\newblock {GAP} package polymaking.
\newblock {\url{http://www.gap-system.org/Packages/polymaking.html}}, 2007.

\bibitem[Rin74]{Ringel74MapColThm}
Gerhard Ringel.
\newblock {\em {M}ap color theorem}.
\newblock Springer-Verlag, New York, 1974.
\newblock Die Grundlehren der mathematischen Wissenschaften, Band 209.

\bibitem[RS72]{Rourke72IntrPLTop}
Colin~P. Rourke and Brian~J. Sanderson.
\newblock {\em {I}ntroduction to piecewise-linear topology}.
\newblock Springer-Verlag, New York, 1972.
\newblock Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69.

\bibitem[Sch94]{Schulz94PolyhMnfPoly}
Christoph Schulz.
\newblock {P}olyhedral manifolds on polytopes.
\newblock {\em Rend. Circ. Mat. Palermo (2) Suppl.}, (35):291--298, 1994.
\newblock First International Conference on Stochastic Geometry, Convex Bodies
  and Empirical Measures (Palermo, 1993).

\bibitem[SK11]{Spreer09CombPorpsOfK3}
Jonathan Spreer and Wolfgang K{\"u}hnel.
\newblock {C}ombinatorial properties of the {K}3 surface: {S}implicial blowups
  and slicings.
\newblock {\em Experiment. Math.}, 20(2):201--216, 2011.

\bibitem[Soi06]{Soicher06GRAPE}
Leonard~H. Soicher.
\newblock {GRAPE - GRaph Algorithms using PErmutation groups}.
\newblock {\url{http://www.gap-system.org/Packages/grape.html}}, 2006.
\newblock {Version 4.3}.

\bibitem[Spa56]{Spanier56HomKummerMnf}
Edwin~H. Spanier.
\newblock {T}he homology of {K}ummer manifolds.
\newblock {\em Proc. AMS}, 7:155--160, 1956.

\bibitem[Spa99]{Sparla99LBTComb2kMnf}
Eric Sparla.
\newblock {A} new lower bound theorem for combinatorial {$2k$}-manifolds.
\newblock {\em Graphs Combin.}, 15(1):109--125, 1999.

\bibitem[Spr10a]{Spreer10Diss}
Jonathan Spreer.
\newblock Blowups, slicings and permutation groups in combinatorial topology,
  2010.
\newblock In preparation.

\bibitem[Spr10b]{Spreer10PartBetaK}
Jonathan Spreer.
\newblock {P}artitioning the triangles of the cross polytope into surfaces.
\newblock {\tt arXiv:1009.2642v1 [math.CO]}, preprint, 12 pages, 1 figure,
  2010.
\newblock {T}o appear in {B}eitr. {A}lgebra {G}eom.

\bibitem[Spr11a]{Spreer11CyclicCombMflds}
Jonathan Spreer.
\newblock Combinatorial 3-manifolds with a cyclic automorphism group.
\newblock Stuttgarter Math. Berichte, 2011/028, 2011.

\bibitem[Spr11b]{Spreer10NormSurfsCombSlic}
Jonathan Spreer.
\newblock {N}ormal surfaces as combinatorial slicings.
\newblock {\em Discrete Math.}, 311(14):1295--1309, 2011.
\newblock {\tt doi:10.1016/j.disc.2011.03.013}.

\bibitem[Spr13]{Spreer12VarCyclPolytope}
Jonathan Spreer.
\newblock {C}ombinatorial seifert fibred spaces with transitive cyclic
  automorphism group, 2013.
\newblock {I}n preparation.

\bibitem[Wee99]{SnapPea}
Jeff Weeks.
\newblock {S}nap{P}ea ({S}oftware for hyperbolic $3$-manifolds), 1999.
\newblock \url{http://www.geometrygames.org/SnapPea/}.

\bibitem[Zie95]{Ziegler95LectPolytopes}
G{\"u}nter~M. Ziegler.
\newblock {\em {L}ectures on polytopes}, volume 152 of {\em Graduate Texts in
  Mathematics}.
\newblock Springer-Verlag, New York, 1995.

\end{thebibliography}
