Some indecomposable polyhedra

Some Indecomposable t-Designs

The existence of large sets of 5-(14,6,3) designs is in doubt. There are five simple 5-(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5(14,6,3) designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states...

Some New Equiprojective Polyhedra

A convex polyhedron P is k-equiprojective if all of its orthogonal projections, i.e., shadows, except those parallel to the faces of P are k-gon for some fixed value of k. Since 1968 it is an open problem to construct all equiprojective polyhedra. Recently, Hasan and Lubiw [8] have given a characterization of equiprojective polyhedra. Based on their characterization, in this paper we discover s...

Indecomposable r-graphs and some other counterexamples

Unfolding some classes of orthogonal polyhedra

In this paper, we study unfoldings of orthogonal polyhedra. More precisely, we deene two special classes of orthogonal polyhedra, orthostacks and orthotubes, and show how to generate unfoldings by cutting faces, such that the resulting surfaces can be attened into a single connected polygon.

Unfolding Lattice Polygons on Some Lattice Polyhedra∗

We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n) moves and time.