Virtual polyhedra models

Education and demonstration – Mathematics – Geometry – trigonometry – or physical mathematic model structure

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G09B 2304

Patent

active

056516797

ABSTRACT:
Kaleidoscopes are used to show solid-appearing images of the Platonic and Archimedean polyhedra (except the snub solids) and of the Kepler-Poinsot stellations. The polyhedra are divided into families related by possessing the same planes of mirror and rotational symmetry, thus using reflectors consisting of three to five mirrors meeting at vertices with specified angles, and corresponding fractions of the solids, such as an octant of the cube for the whole. The fractions may be truncated to form elements representing other members of the families. Slices formed by successive truncations may be superposed to make smaller the elements required. The stellations result from the insertion of the star's "rays" or fractions into reflectors identical with those above. All images appear as solids, not just vertex points, and are viewable over wide angles. The elements are much smaller than the polyhedra, and the reflectors can be folded and/or disassembled for ease of storage and transportation.

REFERENCES:
patent: 718326 (1903-01-01), Diem
patent: 1346017 (1920-07-01), Goodman
patent: 2607142 (1952-08-01), Lee
patent: 5475532 (1995-12-01), Sandoval et al.
Cundy and Rollett, Mathematical Models, Cambridge University Press, 1961, pp. 90-99.

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