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OverviewPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. High Quality Content by WIKIPEDIA articles! In geometry and combinatorics, a simplicial (or combinatorial) d-sphere is a simplicial complex homeomorphic to the d-dimensional sphere. Some simplicial spheres arise as the boundaries of convex polytopes, however, in higher dimensions most simplicial spheres cannot be obtained in this way. The most important open problem in the field is the g-conjecture, formulated by Peter McMullen, which asks about possible numbers of faces of different dimensions of a simplicial sphere.It follows from Euler's formula that any simplicial 2-sphere with n vertices has 3n ae' 6 edges and 2n ae' 4 faces. The case of n = 4 is realized by the tetrahedron. By repeatedly performing the barycentric subdivision, it is easy to construct a simplicial sphere for any n ae 4. Moreover, Ernst Steinitz gave a characterization of 1-skeleta (or edge graphs) of convex polytopes in R3 implying that any simplicial 2-sphere is a boundary of a convex polytope. Full Product DetailsAuthor: Lambert M. Surhone , Miriam T. Timpledon , Susan F. MarsekenPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.60cm , Length: 15.20cm Weight: 0.165kg ISBN: 9786131162664ISBN 10: 6131162662 Pages: 104 Publication Date: 10 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |