| Description |
The basic concepts of linear and affine geometry. Convex sets and their support properties. Supporting hyperplanes. The theorems of Radon, Helly, and Caratheodory. Convex polytopes and their faces. Polarity and duality in convex polytopes. Cell-complexes and Schlegel diagrams. Shelling the boundary complexes. The cubical complexes. The graph of a d-polytope and its properties. 3-polytopes and Steinitz’ theorem. Affine and projective transformations. The fundamental theorem of projective geometry. Simplicial and simple polytopes. Euler’s theorem and the Dehn-Sommerville equations. Lower bound and upper bound theorems for convex polytopes. |