Orihedra: Mathematical sculptures in paper.

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. [ABSTRACT FROM AUTHOR]