- U. Brehm and W. Kühnel,
*Combinatorial manifolds with few vertices*, Topology 26, 465-473 (1987).

- I. Novik,
*Upper bound theorems for homology manifolds*, Israel J. Math. 108, 45-82 (1998) - I. Novik,
*On face numbers of manifolds with symmetry*, Advances Math. 192, 183-208 (2005)

- I. Novik and Ed Swartz,
*Socles of Buchsbaum modules, complexes and posets*, Advances Math. 222, 2059-2084 (2009).

- E. Sparla,
*An upper and a lower bound theorem for combinatorial $4$-manifolds*, Discrete Comp. Geom. 19, 575-593 (1998) - E. Sparla,
*A new lower bound theorem for combinatorial $2k$-manifolds*, Graphs and Combinatorics 15, 109-125 (1999)

- W. Kühnel,
*Tight polyhedral submanifolds and tight triangulations*, Lecture Notes in mathematics 1612, 122 pages, Springer 1995

- M. Casella and W. Kühnel,
*A triangulated K3 surface with the minimum number of vertices*, Topology 40, 753-772 (2001) - W. Kühnel and F. H. Lutz,
*A census of tight triangulations*, Periodica Math. Hungarica 39, 161-183 (1999) - W. Kühnel,
*Tight embeddings of simply connected $4$-manifolds*, Documenta Math. 9, 401-412 (2004) (electronic)

- W. Kühnel,
*Centrally-symmetric tight surfaces and graph embeddings*, Beiträge zur Algebra und Geometrie 37, 347-354 (1996) - F. Effenberger and W. Kühnel,
*Hamiltonian submanifolds of regular polytopes*, Discrete Comput. Geometry 43, 242-262 (2010)

- F. Effenberger,
*Stacked polytopes and tight triangulations of manifolds,*J. Comb. Theory, Ser. A 118, No. 6, 1843-1862 (2011) - F. Effenberger,
*Hamiltonian submanifolds of regular polytopes*, Doctoral Thesis, Stuttgart 2010

- Find triangulations of 2k-manifolds with 3k+3 vertices.
This is the minimum number for any manifold which is not a sphere, see
- U. Brehm and W. Kühnel,
*Combinatorial manifolds with few vertices*, Topology 26, 465-473 (1987)

- U. Brehm and W. Kühnel,
- Find tight polyhedral embeddings of the projective planes
over the real, complex numbers, quaternions, or octonions
in the same codimension as the classical Veronese-type embeddings of them.
Halfway between two antipodal copies of them we find polyhedral
analogous of the Cartan isoparametric hypersurfaces in spheres
(which are tubes around the Veronese-type embeddings), see
- T.F. Banchoff and W. Kühnel,
*Tight polyhedral models of isoparametric families, and PL--taut submanifolds*,

Advances in Geometry 7, 613--639 (2007)

- T.F. Banchoff and W. Kühnel,
- Find triangulated (pseudo-)manifolds satisfying the following
combinatorial complementarity condition:
- A subset $A \subset V$ of the set of vertices V spans a simplex if and only if the complement $V \setminus A$ does not.

- U. Brehm and W. Kühnel,
*$15$-vertex triangulations of an $8$-manifold*, Math. Annalen 294, 167-193 (1992)

- W. Kühnel and G. Lassmann,
*Combinatorial $d$-tori with a large symmetry group*, Discrete Comp. Geom. 3, 169-176 (1988) - G. Dartois and A. Grigis,
*Separating maps of the lattice $E$*, Discrete Comp. Geom. 23, 555-567 (2000)_{8}and triangulations of the eight-dimensional torus

- U. Brehm and W. Kühnel,
*Lattice triangulations of $E3$ and of the 3-torus*, Israel J. Math. 189, 97-133 (2012).

- P. McMullen and E. Schulte,
*Abstract Regular Polytopes*, 570 pages, Cambridge University Press 2001

- U. Brehm, W. Kühnel and E. Schulte,
*Manifold structures on abstract regular polytopes*, Aequationes math. 49, 12-35 (1995)