## Orihedra: Mathematical Sculptures in Paper (1997)

Venue: | International Journal of Computers for Mathematical Learning |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Eisenberg97orihedra:mathematical,

author = {Michael Eisenberg and Ann Nishioka},

title = {Orihedra: Mathematical Sculptures in Paper},

journal = {International Journal of Computers for Mathematical Learning},

year = {1997},

volume = {1},

pages = {225--261}

}

### OpenURL

### Abstract

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.

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Citation Context ... cuboctahedron and icosidodecahedron may be "sliced in two" to produce half-shapes (the first including an equatorial hexagon that can be seen in the original shape, the second an equatorial decagon [=-=Coxeter, 1973-=-]); such operations are staples of our own polyhedral sculptural design. More generally, polyhedral sculpture provides a fertile context in which to explore patterns in polyhedra: how they can be stre... |

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Citation Context ... of mathematical manipulatives as tangible representatives of abstract concepts [cf. WelchmanTischler, 1992]; the "constructionist" approach to learning as mediated through the creation of artifacts [=-=Papert, 1991-=-]; the social or emotional role that physical objects are capable of playing in students' lives [Eisenberg and DiBiase, 1996]; and the creative benefits of computational media (with an emphasis on the... |

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Citation Context ...ive and from the "engineering" perspective inherent in sculptural work. 9 A tool similar in operation to the one proposed here was developed for an earlier Scheme-based application named SchemeChart [=-=Eisenberg and Fischer, 1994-=-]. Eisenberg/Nishioka—30sFigure 23. A small rhombicosidodecahedron (left) has a group of 11 faces removed to produce a new shape with a decagonal face (right). 5.2 Related work In the previous section... |

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Citation Context ...e as a pen. Toward the center of the figure, still another face of the folding net in the figure has been decorated using a turtlegraphics pattern—a "rotated polygon" figure of the kind described in [=-=Abelson and diSessa, 1980-=-]. In short, then, the decorative techniques available in HyperGami span a wide range, including techniques available through palette selection and Scheme language expressions. Beyond this brief descr... |

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Citation Context ...ulptures derive from observing forms in the real world, and then attempting to "analyze" those shapes into polyhedral forms. (Similar ideas for sculpting and three-dimensional design may be found in [=-=Pearce and Pearce, 1980-=-].) Often—as in the penguin sculptures—we have found that combinations of relatively simple shapes are able to suggest interesting subjects: the mushrooms of Figure 14 and fish of Figure 15 are made, ... |

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