Poly is a shareware program for exploring and constructing polyhedra. With Poly, you can manipulate polyhedral solids on the computer in a variety of ways. Flattened versions (nets) of polyhedra may be printed and then cut out, folded, and taped, to produce three-dimensional models. Unregistered copies are fully-functional, but Pedagoguery asks users to remember that Poly is for evaluation purposes only until you have registered.

Poly offers an English, a Spanish, a French, and a Korean interface.

Poly System Requirements:
680x0 Macintosh 68000 - 68040 System 6 - MacOS 8.1
Power Macintosh Any PowerMac System 7.1.2 - MacOS 9.0
(Windows versions also available)

Poly includes all of the following polyhedra:

Platonic Solids
Each platonic polyhedron is constructed using (multiple copies of) a single regular polygon; the same number of polygonal faces is used around each vertex. A polygon is regular if all of its edges have the same length and all of its interior angles are equal. Both the equilateral triangle and square are regular polygons.

Archimedean Solids
The Archimedean solids were defined historically by Archimedes, although we have lost his writings. All of the Archimedean solids are uniform polyhedra with regular faces. A polyhedron with regular polygonal faces is uniform if there are symmetry operations that take one vertex through all of the other vertices and no other points in space. For example, the cube has rotation by 90° around an axis and reflection through a plane perpendicular to that axis as its symmetry operations. A common heuristic for the Archimedean solids is that the arrangement of faces surrounding each vertex must be the same for all vertices. Although all of the Archimedean solids have this property, so does the elongated square gyrobicupola (Johnson solid which is not an Archimedean solid.

Prisms and Anti-Prisms
After the Platonic and Archimedean solids, the only remaining convex uniform polyhedra with regular faces are prisms and anti-prisms. This was shown by Johannes Kepler, who also gave the names commonly used for the Archimedean solids.

Johnson Solids
After taking into account the preceeding three categories, there are only a finite number of convex polyhedra with regular faces left. The enumeration of these polyhedra was performed by Norman W. Johnson.

Catalan Solids
The Catalan solids are duals of Archimedean solids. A dual of a polyhedron is constructed by replacing each face with a vertex, and each vertex with a face. For example, the dual of the icosahedron is the dodecahedron; the dual of the dodecahedron is the icosahedron.

Dipyramids and Deltohedrons
Dipyramids are duals of prisms; deltohedrons are duals of anti-prisms.

For more information, visit:
http://www.peda.com/poly/

Dipyramids are duals of prisms; deltohedrons are duals of anti-prisms.

Charles W. Moore

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February 09, 2010