Wrapping the cube and other polyhedra
نویسندگان
چکیده
منابع مشابه
Uniqueness of Optimal Cube Wrapping
Consider wrapping the unit cube with a square without stretching or cutting. Beebee demonstrated such a wrapping with a square of side length 2 √ 2, and proved that no smaller square can fulfill the task [1]. We show that Beebee’s construction is the unique optimal wrapping, up to the symmetries of the unit cube and the placement of the junk material.
متن کاملFullerenes and coordination polyhedra versus half-cube embeddings
A fullerene F, is a 3-regular (or cubic) polyhedral carbon molecule for which the n vertices the carbons atoms are arranged in 12 pentagons and (n/210) hexagons. Only a finite number of fullerenes are expected to be, up to scale, isometrically embeddable into a hypercube. Looking for the list of such fullerenes, we first check the embeddability of all fullerenes F, for n < 60 and of all prefera...
متن کاملExact join detection for convex polyhedra and other numerical abstractions
Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification and optimization of hardware and software systems. In such application fields though, general convex polyhedra are just one among many, so-called, numerical a...
متن کاملPossibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
The domain of convex polyhedra is employed in several systems for the analysis and verification of hardware and software components. Current applications span imperative, functional and logic languages, synchronous languages and synchronization protocols, real-time and hybrid systems. Since the seminal work of P. Cousot and N. Halbwachs, convex polyhedra have thus played an important role in th...
متن کاملWrapping the future
Enclosing a component within a software “wrapper” is a well-established way of adapting components for use in new environments. This paper presents an overview of an experimental evaluation of the use of a wrapper to protect against faults arising during the (simulated) operation of a practical and critical system; the specific context is a protective wrapper for an off-the-shelf software compo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2012
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2012.0116