Determining the Castability of Simple Polyhedra

Determining the Symmetry of Polyhedra

Tetrahedralization of Simple and Non-Simple Polyhedra

It is known that not all simple polyhedra can be tetrahedralized, i.e., decomposed into a set of tetrahedra without adding new vertices (tetrahedralization). We investigate several classes of simple and non-simple polyhedra that admit such decompositions. In particular, we show that certain classes of rectilinear (isothetic) simple polyhedra can always be tetrahedralized in O(n2) time where n i...

Determining the Separation of Preprocessed Polyhedra - A Unified Approach

We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries e ciently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) app...

Simple equations giving shapes of various convex polyhedra: the regular polyhedra and polyhedra composed of crystallographically low-index planes

Simple equations are derived that give the shapes of various convex polyhedra. The five regular polyhedra, called Platonic solids (the tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and polyhedra composed of crystallographically low-index planes are treated. The equations also give shapes that are nearly polyhedral with round edges, or intermediate shapes between a ...

Zigzag Structures of Simple Two-Faced Polyhedra

A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigzag and railroad structures of general 3-valent plane graph and, especially, o...