In 1997 the most prestigious high school science fair in the United States—the Westinghouse Science Competition [Berger 94] —was won by Adam Cohen, then a senior at Hunter High School in New York City. Cohen's project, "Near-Field Photolithography", involved the construction of a home-built scanning tunneling microscope (or STM—a high-resolution

In 1525, the painter Albrecht Dürer introduced the notion of a net of a polytope, and published nets for some of the Platonian and Archimedian polyhedra, along with directions about how to construct them. An unfolding of a 3-dimensional polytope P is obtained by cutting the boundary of P along a collection of edges that spans the vertex set of P and then flattening the remaining set to a polygon in the plane. An unfolding is a net if it does not overlap itself. Conversely, a simple connected plane polygon with specific folding lines is a net, if it is possible to fold it into (the boundary of) a polytope. We consider the question whether every 3-dimensional polytope has a net. Although the problem is intuitive and easy to state, and there are nets known for all regular and uniform polytopes, in general it is still unsolved. After giving an overview of related questions and conjectures about the nature or existence of nets for 3-polytopes, we present an account of our experiments wit...

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As I write this sentence, I am glancing over at the color printer sitting beside my screen. In the popular jargon of the computer industry, that printer is called a "peripheral"—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ultimate

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Mathematics, as a subject dealing with abstract concepts, poses a special challenge for educators. In students ' experience, the subject is often associated with (potentially) unflattering adjectives—"austere", "remote", "depersonalized", and so forth. This paper describes a computer program named HyperGami whose purpose is to alleviate this harsh portrait of the mathematical enterprise. HyperGami is a system for the construction of decorated paper polyhedral shapes; these shapes may be combined into larger polyhedral sculptures, which we have dubbed "orihedra. " In this paper, we illustrate the methods by which orihedra may be created from HyperGami solids (using the construction of a particular sculpture as an example); we describe our experiences with elementary- and middle-school students using HyperGami to create orihedra; we discuss the current limitations of HyperGami as a sculptural medium; and we outline potential directions for future research and software development.