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<h3>References</h3>

<a id="biBBanchoff65TightEmb3DimPolyMnf" name="biBBanchoff65TightEmb3DimPolyMnf"></a>

[Ban65] Banchoff, T. F.,
Tightly embedded 2-dimensional polyhedral
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Amer. J. Math.,
87
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462--472.


<a id="biBBanchoff74TightPolyKBProjPMB" name="biBBanchoff74TightPolyKBProjPMB"></a>

[Ban74] Banchoff, T. F.,
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<a id="biBregina" name="biBregina"></a>

[BBP+14] Burton, B. A., Budney, R., Pettersson, W. and others,,
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[BD11] Bagchi, B. and Datta, B.,
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A characterization of tightly triangulated 3-manifolds
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[BL98] Breuer, T. and Linton, S.,
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[BL14b] K. Adiprasito B. Benedetti, and Lutz, F. H.,
Random Discrete Morse Theory II and a Collapsible 5-Manifold
 Different from the 5-Ball.
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 tables.


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[BR08] Barakat, M. and Robertz, D.,
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<a id="biBSpreer12VarCyclPolytope" name="biBSpreer12VarCyclPolytope"></a>

[BS14] Burton, B. A. and Spreer, J.,
Combinatorial Seifert fibred spaces with transitive cyclic
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 Mathematics),
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[CK01] Casella, M. and K{\"u}hnel, W.,
A triangulated K3 surface with the minimum
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Topology,
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[Con09] Conder, M. D. E.,
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[Dat07] Datta, B.,
Minimal triangulations of manifolds,
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429--449.


<a id="biBDumas04Homology" name="biBDumas04Homology"></a>

[DHSW11] Dumas, J. -.G., Heckenbach, F., Saunders, B. D. and Welker, V.,
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{\url{http://www.cis.udel.edu/~dumas/Homology/}}.


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[DKT08] Desbrun, M., Kanso, E. and Tong, Y.,
Discrete differential forms for computational modeling,
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<a id="biBEffenberger10Diss" name="biBEffenberger10Diss"></a>

[Eff11a] Effenberger, F.,
Hamiltonian submanifolds of regular polytopes,
Logos Verlag, Berlin
(2011) 
(Dissertation, University of Stuttgart, 2010).


<a id="biBEffenberger09StackPolyTightTrigMnf" name="biBEffenberger09StackPolyTightTrigMnf"></a>

[Eff11b] Effenberger, F.,
Stacked polytopes and tight triangulations of
 manifolds,
Journal of Combinatorial Theory, Series A,
118 (6)
(2011),
1843 - 1862.


<a id="biBEngstroem09DiscMorseFuncFourierTrans" name="biBEngstroem09DiscMorseFuncFourierTrans"></a>

[Eng09] Engstr{\"o}m, A.,
Discrete Morse functions from Fourier
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Experiment. Math.,
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<a id="biBForman95DiscrMorseTheoryCellCompl" name="biBForman95DiscrMorseTheoryCellCompl"></a>

[For95] Forman, R.,
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<a id="biBFrohmader08FaceVecFlagCompl" name="biBFrohmader08FaceVecFlagCompl"></a>

[Fro08] Frohmader, A.,
Face vectors of flag complexes,
Israel J. Math.,
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<a id="biBJoswig00Polymake" name="biBJoswig00Polymake"></a>

[GJ00] Gawrilow, E. and Joswig, M.,
polymake: a framework for analyzing convex polytopes,
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<a id="biBGruenbaum03ConvPoly" name="biBGruenbaum03ConvPoly"></a>

[Gr\03] Gr{\"u}nbaum, B.,
Convex polytopes,
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221,
New York
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<a id="biBM2" name="biBM2"></a>

[GS] Grayson, D. R. and Stillman, M. E.,
Macaulay2, a software system for research
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[Hak61] Haken, W.,
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245--375.


<a id="biBHauser2000" name="biBHauser2000"></a>

[Hau00] Hauser, H.,
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<a id="biBHirzebruch1953" name="biBHirzebruch1953"></a>

[Hir53] Hirzebruch, F. E. P.,
\"Uber vierdimensionale Riemannsche Fl\"achen mehrdeutiger
 analyti\-scher
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<a id="biBHopf1951" name="biBHopf1951"></a>

[Hop51] Hopf, H.,
\"Uber komplex-analytische Mannigfaltigkeiten,
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[Hud69] Hudson, J. F. P.,
Piecewise linear topology,
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University of Chicago Lecture Notes prepared with the assistance
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<a id="biBHuppert67EndlGruppen" name="biBHuppert67EndlGruppen"></a>

[Hup67] Huppert, B.,
Endliche Gruppen. I,
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Berlin
(1967),
xii+793 pages.


<a id="biBKuehnel99CensusTight" name="biBKuehnel99CensusTight"></a>

[KL99] K{\"u}hnel, W. and Lutz, F. H.,
A census of tight triangulations,
Period. Math. Hungar.,
39 (1-3)
(1999),
161--183 
({D}iscrete geometry and rigidity ({B}udapest, 1999)).


<a id="biBKlee11CentSymmMnfFewVert" name="biBKlee11CentSymmMnfFewVert"></a>

[KN12] Klee, S. and Novik, I.,
Centrally symmetric manifolds with few vertices,
Adv. Math.,
229 (1)
(2012),
487--500.


<a id="biBKneser29ClosedSurfIn3Mflds" name="biBKneser29ClosedSurfIn3Mflds"></a>

[Kne29] Kneser, H.,
Geschlossene Fl\"achen in dreidimensionalen
 Mannigfaltigkeiten,
Jahresbericht der deutschen Mathematiker-Vereinigung,
38
(1929),
248--260.


<a id="biBKirby77PLStructures" name="biBKirby77PLStructures"></a>

[KS77] Kirby, R. C. and Siebenmann, L. C.,
Foundational essays on topological manifolds, smoothings, and
 triangulations,
Princeton University Press, Princeton, N.J.; University of
 Tokyo Press, Tokyo
(1977),
vii+355 pages 
(With notes by John Milnor and Michael Atiyah,
 Annals of Mathematics Studies, No. 88).


<a id="biBKuehnel86HigherDimCsaszar" name="biBKuehnel86HigherDimCsaszar"></a>

[K\t86] K{\"u}hnel, W.,
Higher dimensional analogues of
 Cs\'asz\'ar's torus,
Results Math.,
9
(1986),
95--106.


<a id="biBKuehnel94ManSkelConvPolyt" name="biBKuehnel94ManSkelConvPolyt"></a>

[K\t94] K{\"u}hnel, W.,
Manifolds in the skeletons of convex polytopes, tightness, and
generalized Heawood inequalities,
 in Polytopes: abstract, convex and computational (Scarborough, ON,
 1993),
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440,
Dordrecht
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<a id="biBKuehnel95TightPolySubm" name="biBKuehnel95TightPolySubm"></a>

[K\t95] K{\"u}hnel, W.,
Tight polyhedral submanifolds and tight triangulations,
Springer-Verlag,
Lecture Notes in Mathematics,
1612,
Berlin
(1995),
vi+122 pages.


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[Kui84] Kuiper, N. H.,
Geometry in total absolute curvature theory,
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<a id="biBLutz08ManifoldPage" name="biBLutz08ManifoldPage"></a>

[Lut] Lutz, F. H.,
The Manifold Page,
{\url{http://www.math.tu-berlin.de/diskregeom/stellar}}.


<a id="biBLutz03TrigMnfFewVertVertTrans" name="biBLutz03TrigMnfFewVertVertTrans"></a>

[Lut03] Lutz, F. H.,
Triangulated Manifolds with Few Vertices
 and Vertex-Transitive
Group Actions,
Ph.D. thesis,
TU Berlin
(2003).


<a id="biBLutz05TrigMnfFewVertCombMnf" name="biBLutz05TrigMnfFewVertCombMnf"></a>

[Lut05] Lutz, F. H.,
Triangulated Manifolds with Few Vertices:
 Combinatorial
Manifolds
(2005),
{\tt arXiv:math/0506372v1 [math.CO]}, Preprint, 37
 pages.


<a id="biBMcKay84Nauty" name="biBMcKay84Nauty"></a>

[MP14] McKay, B. D. and Piperno, A.,
Practical graph isomorphism, \II\ ,
Journal of Symbolic Computation ,
60 (0)
(2014),
94 - 112.


<a id="biBPachner87KonstrMethKombHomeo" name="biBPachner87KonstrMethKombHomeo"></a>

[Pac87] Pachner, U.,
Konstruktionsmethoden und das kombinatorische
 Hom\"oomorphieproblem
 f\"ur Triangulierungen kompakter semilinearer
 Mannigfaltigkeiten,
Abh. Math. Sem. Uni. Hamburg,
57
(1987),
69--86.


<a id="biBPaixao143SphereRec" name="biBPaixao143SphereRec"></a>

[PS15] Paix{\~a}o, J. and Spreer, J.,
Random collapsibility and 3-sphere recognition
(2015) 
(Preprint, 18 pages, 6 figures),
\texttt{arXiv:1509.07607 [math.GT]}.


<a id="biBRingel74MapColThm" name="biBRingel74MapColThm"></a>

[Rin74] Ringel, G.,
Map color theorem,
Springer-Verlag,
New York
(1974),
xii+191 pages 
(Die Grundlehren der mathematischen Wissenschaften, Band 209).


<a id="biBRourke72IntrPLTop" name="biBRourke72IntrPLTop"></a>

[RS72] Rourke, C. P. and Sanderson, B. J.,
Introduction to piecewise-linear topology,
Springer-Verlag,
New York
(1972),
viii+123 pages 
(Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69).


<a id="biBRoeder07Polymaking" name="biBRoeder07Polymaking"></a>

[R\t13] R\"{o}der, M.,
GAP package polymaking
(2013),
{\url{https://www.gap-system.org/Packages/polymaking.html}}.


<a id="biBSchulz94PolyhMnfPoly" name="biBSchulz94PolyhMnfPoly"></a>

[Sch94] Schulz, C.,
Polyhedral manifolds on polytopes,
Rend. Circ. Mat. Palermo (2) Suppl. (35)
(1994),
291--298 
(First International Conference on Stochastic Geometry, Convex Bodies
and Empirical Measures (Palermo, 1993)).


<a id="biBSpreer09CombPorpsOfK3" name="biBSpreer09CombPorpsOfK3"></a>

[SK11] Spreer, J. and K{\"u}hnel, W.,
Combinatorial properties of the K3 surface:
 Simplicial blowups
and slicings,
Experiment. Math.,
20 (2)
(2011),
201--216.


<a id="biBSoicher06GRAPE" name="biBSoicher06GRAPE"></a>

[Soi12] Soicher, L. H.,
GRAPE - GRaph Algorithms using PErmutation groups
(2012) 
({Version 4.6.1}),
{\url{https://www.gap-system.org/Packages/grape.html}}.


<a id="biBSpanier56HomKummerMnf" name="biBSpanier56HomKummerMnf"></a>

[Spa56] Spanier, E. H.,
The homology of Kummer manifolds,
Proc. AMS,
7
(1956),
155--160.


<a id="biBSparla99LBTComb2kMnf" name="biBSparla99LBTComb2kMnf"></a>

[Spa99] Sparla, E.,
A new lower bound theorem for combinatorial
 2k-manifolds,
Graphs Combin.,
15 (1)
(1999),
109--125.


<a id="biBSpreer10Diss" name="biBSpreer10Diss"></a>

[Spr11a] Spreer, J.,
Blowups, slicings and permutation groups in combinatorial
 topology,
Ph.D. thesis,
Logos Verlag Berlin,
University of Stuttgart
(2011),
251 pages 
(Ph.D. thesis).


<a id="biBSpreer10NormSurfsCombSlic" name="biBSpreer10NormSurfsCombSlic"></a>

[Spr11b] Spreer, J.,
Normal surfaces as combinatorial slicings,
Discrete Math.,
311 (14)
(2011),
1295--1309 
({\tt doi:10.1016/j.disc.2011.03.013}).


<a id="biBSpreer10PartBetaK" name="biBSpreer10PartBetaK"></a>

[Spr12] Spreer, J.,
Partitioning the triangles of the cross polytope into
 surfaces,
{Beitr. Algebra Geom. / Contributions to Algebra and
 Geometry},
53 (2)
(2012),
473--486.


<a id="biBSpreer11CyclicCombMflds" name="biBSpreer11CyclicCombMflds"></a>

[Spr14] Spreer, J.,
Combinatorial 3-manifolds with transitive cyclic symmetry,
Discrete Comput. Geom.,
51 (2)
(2014),
394--426.


<a id="biBSnapPea" name="biBSnapPea"></a>

[Wee99] Weeks, J.,
SnapPea (Software for hyperbolic
 3-manifolds)
(1999) 
(\url{http://www.geometrygames.org/SnapPea/}).


<a id="biBWilson96UST" name="biBWilson96UST"></a>

[Wil96] Wilson, D. B.,
Generating random spanning trees more quickly than the cover
 time,
 in Proceedings of the Twenty-eighth Annual ACM
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 on the Theory of Computing (Philadelphia, PA,
 1996),
ACM, New York
(1996),
296--303.


<a id="biBZiegler95LectPolytopes" name="biBZiegler95LectPolytopes"></a>

[Zie95] Ziegler, G. M.,
Lectures on polytopes,
Springer-Verlag,
Graduate Texts in Mathematics,
152,
New York
(1995),
x+370 pages.


 

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