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Neighborly 2-Manifolds with 12 Vertices
A complete list of 59 orientable neighborly 2-manifolds with 12 vertices of genus 6 is provided, and their possible flat embeddings in Euclidean 3-space are studied.
On the Finding of Final Polynomials
An infinite family of minor-minimal nonrealizable 3-chirotopes
The classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes
Nonrealizability proofs in computational geometry
This paper resolves a problem posed in  by proving that not every realizable simplicial chirotope admits a solvability sequence and shows that there is no easy combinatorial method for proving nonrealizability and thus justifies the final polynomial approach.
On Heuristic Methods for Finding Realizations of Surfaces
- J. Bokowski
Heuristic methods for finding realizations of oriented matroids of rank 3 and 4 can be applied for the spatial embeddability problem of 2-manifolds.
On the Generation of Oriented Matroids
It is shown that there exists an infinite class of orientable triangulated closed 2-manifolds for each genus g \geq 6 that cannot be embedded geometrically in Euclidean 3-space.
On combinatorial and affine automorphisms of polytopes
We disprove the longstanding conjecture that every combinatorial automorphism of the boundary complex of a convex polytope in euclidean spaceEd can be realised by an affine transformation ofEd.
Neighborly 6-polytopes with 10 vertices
There are exactly 37 combinatorial types of neighborly 6-polytopes with 10 vertices. A full description is given.
On a Mutation Problem for Oriented Matroids
For uniform oriented matroids M with n elements, there is in the realizable case a sharp lower bound Lr(n) for the number mut(M) of mutations of M: Lr(n) =n?mut(M), see Shannon 17]. Finding a sharp…