The continuous symmetry methodology has been developed to provide a quantitative estimation for the degree of a selected symmetry point-group in a molecular structure. Previous developed measures included the C(S), C(n), S(n) (including C(i)) symmetries, several polyhedral symmetries, and the related chirality measure. Motivated by the abundance and importance of C(nv) symmetry in many key mole...

Extensions to classical Octrees that add new types of terminal nodes have been proposed for the exact representation of polyhedral objects. In this work, we present a new solid representation scheme using Octrees, which include boundary information of the represented object in the internal nodes of the tree. In this way, basic operations with the model will be accelerated and we are able to rep...

Some engineering applications require structures to expand and contract in size, while retaining their exterior shape. The applications range from mundane daily life objects to more fancy art structures. In contrast to a multi degree-of-freedom structure, a single degree-of-freedom structure can be driven by a single actuator, reducing cost and simplifying the control. In this paper, we study s...

We study the following problem: Given a collection A of polyhedral parts in 3D, determine whether there exists a subset S of the parts that can be moved as a rigid body by an innnitesimal translation and rotation , without colliding with the rest of the parts, A n S. A negative result implies that the object whose constituent parts are the collection A cannot be taken apart with two hands. A po...

The Sparse Polyhedral Framework (SPF) extends the Polyhedral Model by using the uninterpreted function call abstraction for the compile-time specification of run-time reordering transformations such as loop and data reordering and sparse tiling approaches that schedule irregular sets of iteration across loops. The Polyhedral Model represents sets of iteration points in imperfectly nested loops ...

In [2], a {5, 5}-equivelar polyhedral map of Euler characteristic −8 was constructed. In this article we prove that {5, 5}-equivelar polyhedral map of Euler characteristic −8 is unique. As a consequence, we get that the minimum number of edges in a non-orientable polyhedral map of Euler characteristic −8 is > 40. We have also constructed {5, 5}-equivelar polyhedral map of Euler characteristic −...