Polyhedral Suspensions of Arbitrary Genus
نویسنده
چکیده
A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial definition of a polyhedral suspension is given. A new regular 2-dimensional polyhedron is constructed in four dimensions. Short running title: Polyhedral suspensions. 2000 AMS Subject Classification: Primary: 57M20; Secondary: 05C10, 90C57, 52B05, 52B70, 57M15, 51M20, 51M04, 55P40.
منابع مشابه
Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
Compact polyhedral surfaces (or, equivalently, compact Riemann surfaces with conformal flat conical metrics) of an arbitrary genus are considered. After giving a short self-contained survey of their basic spectral properties, we study the zeta-regularized determinant of the Laplacian as a functional on the moduli space of these surfaces. An explicit formula for this determinant is obtained.
متن کاملPolyhedral Embeddings of Snarks with Arbitrary Nonorientable Genera
Mohar and Vodopivec [Combinatorics, Probability and Computing (2006) 15, 877-893] proved that for every integer k (k > 1 and k 6= 2), there exists a snark which polyhedrally embeds in Nk and presented the problem: Is there a snark that has a polyhedral embedding in the Klein bottle? In the paper, we give a positive solution of the problem and strengthen Mohar and Vodopivec’s result. We prove th...
متن کاملApproximate Shortest Path Queries on Weighted Polyhedral Surfaces
We consider the classical geometric problem of determining shortest paths between pairs of points lying on a weighted polyhedral surface P consisting of n triangular faces. We present query algorithms that compute approximate distances and/or approximate (weighted) shortest paths. Our algorithm takes as input an approximation parameter ε ∈ (0, 1) and a query time parameter q and builds a data s...
متن کاملCasting a Polyhedron with Directional Uncertainty
Casting is a manufacturing process in which molten material is poured into a cast (mould), which is opened after the material has solidified. As in all applications of robotics, we have to deal with imperfect control of the casting machinery. In this paper, we consider directional uncertainty: given a 3-dimensional polyhedral object, is there a polyhedral cast such that its two parts can be rem...
متن کاملA Distinct Element Granular Solver/fictitious Domain Method for the Numerical Simulation of Particulate Flows
In the Oil and Gas industry, many situations are representative of particulate flows : cutting removal in drilling operations, sand management in production, dispersed hydrates transportation in pipeline, ... Particles may be of arbitrary shape and the fluid itself may exhibit non-Newtonian properties. To enhance the comprehension of complex phenomena occurring in moderately or highly concentra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 26 شماره
صفحات -
تاریخ انتشار 2010