论文信息 - A criterion for the affine equivalence of cell complexes inRd and convex polyhedra inRd+1

A criterion for the affine equivalence of cell complexes inRd and convex polyhedra inRd+1

A criterion is given that decides, for a convex tilingC ofRd, whetherC is the projection of the faces in the boundary of some convex polyhedronP inRd+1. Its applicability is restricted neither by the properties nor by the dimension ofC. It turns out to be conceptually simpler than other criteria and allows the easy examination of various classes of cell complexes. In addition, the criterion is constructive, that is, it can be used to constructP provided it exists.

Franz Aurenhammer | F. Aurenhammer

[1] Frank Harary,et al. Graph Theory , 2016 .

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

[3] Franz Aurenhammer,et al. Recognising Polytopical Cell Complexes and Constructing Projection Polyhedra , 1987, J. Symb. Comput..

[4] Herbert Edelsbrunner,et al. Finding Extreme Points in Three Dimensions and Solving the Post-Office Problem in the Plane , 1985, Inf. Process. Lett..

[5] Franz Aurenhammer,et al. Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[6] R. Connelly,et al. A convex 3-complex not simplicially isomorphic to a strictly convex complex , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[7] J. Maxwell,et al. I.—On Reciprocal Figures, Frames, and Diagrams of Forces , 1870, Transactions of the Royal Society of Edinburgh.

[8] Franz Aurenhammer. A New Duality Result Concerning Voronoi Diagrams , 1986, ICALP.

[9] W. Blaschke. Vorlesungen über Differentialgeometrie , 1912 .

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

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

[12] H. Pollaczek-Geiringer,et al. W. Blaschke, Vorlesungen über Differentialgeometrie I. 2. Auflage (Grundlehren der math. Wiss. in Einzeldarstellungen, Bd. I). Verlag J. Springer, Berlin 1924 , 1925 .