A convex 3-complex not simplicially isomorphic to a strictly convex complex

A set X in euclidean space is convex if the line segment joining any two points of X is in X. If X is convex, every boundary point is on an (n − 1)-plane which contains X in one of its two closed half-spaces. Such a plane is called a support plane for X. A simplicial complex K in is called strictly convex if |K| (the underlying space of K) is convex and if, for every simplex σ in ∂K (the boundary of K) there is a support plane for |K| whose intersection with |K| is precisely σ In this case |K| is often called a simplicial polytope.

[1]  Christoph Schulz.  An invertable 3-diagram with 8 vertices , 1979, Discret. Math..

[2]  G. C. Shephard,et al.  Stellar subdivisions of boundary complexes of convex polytopes , 1974 .

[3]  P. Mani,et al.  Spheres with Few Vertices , 1972, J. Comb. Theory A.

[4]  C. Rourke,et al.  Introduction to Piecewise-Linear Topology , 1972 .

[5]  P. Mani,et al.  Shellable Decompositions of Cells and Spheres. , 1971 .

[6]  G. C. Shephard.  Spherical complexes and radial projections of polytopes , 1971 .

[7]  P. McMullen.  The maximum numbers of faces of a convex polytope , 1970 .

[8]  W. B. R. Lickorish,et al.  Triangulations of the $3$-ball with knotted spanning $1$-simplexes and collapsible $r$th derived subdivisions , 1969 .

[9]  Richard E. Goodrick,et al.  Non-simplicially collapsible triangulations of In , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  B. Grünbaum,et al.  An enumeration of simplicial 4-polytopes with 8 vertices , 1967 .

[11]  D. R. J. Chillingworth,et al.  Collapsing three-dimensional convex polyhedra , 1967, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  E. C. Zeeman,et al.  Seminar on combinatorial topology , 1963 .

[13]  R. Bing.  An Alternative Proof that 3-Manifolds Can be Triangulated , 1959 .

[14]  Mary Ellen Rudin,et al.  An unshellable triangulation of a tetrahedron , 1958 .

[15]  Fred Supnick.  On the Perspective Deformation of Polyhedra , 1948 .

[16]  G. T. Whyburn,et al.  Lectures in topology , 1942 .

[17]  Triangulated Manifolds Which are Not Brouwer Manifolds , 1940 .

[18]  On Subdivisions of Complexes , 1935 .

[19]  J. Maxwell,et al.  XLV. On reciprocal figures and diagrams of forces , 1864 .