Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which ...

A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...

A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the case we treat in this paper. The conceptually simplest mechanism for correcting errors in a cellular automaton is to determine the next state of a cell by ta...

A set V of nondegenerate convex polygons P in R, or polyhedra P in R, will be called normal if the intersection of any two of the P's of V is a face (in the case of polyhedra), an edge, a vertex, or empty. V is called strongly normal (SN) if it is normal and, for all P, Pi,..., Pn, if each P; intersects P and / = Px f) ... f~l Pn is nonempty, then I intersects P. The union of the Pt€ V that int...

Let ∆ = ∆(a, b, c) be a hyperbolic triangle group, a Fuchsian group obtained from reflections in the sides of a triangle with angles π/a, π/b, π/c drawn on the hyperbolic plane. We define the arithmetic dimension of ∆ to be the number of split real places of the quaternion algebra generated by ∆ over its (totally real) invariant trace field. Takeuchi has determined explicitly all triples (a, b,...

In this study, two-dimensional finite element modeling was used to study the simultaneous effect of the cell shape and regular cell distribution on the anisotropy of the elastic properties of 316L stainless steel foam. In this way, the uniaxial compressive stress-strain curve was predicted using a geometric model and fully solid 316L stainless steel. The results showed that the elastic tangent ...

Random tessellations form a very important field in stochastic geometry. They pose many interesting mathematical problems and have numerous important applications in many branches of natural sciences and engineering, as this volume shows. This contribution aims to present mathematical basic facts as well as statistical ideas for random tessellations of the d-dimensional Euclidean space R. Havin...