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Conway polyhedron notation is used to describe Polyhedra based on a seed polyhedron modified by various Operator s. The seed polyhedra are the Platonic Solid s, represented by their first letter of their name (T,O,C,I,D); the Prism s (P''n''), Antiprism s (A''n'') and Pyramid s (Y''n''). Any convex polyhedron can serve as a seed, as long as the operations can be executed on it. John Conway extended the idea of using operators, like Truncation defined by Kepler , to build related polyhedra of the same symmetry. His descriptive operators that can generate all the Archimedean Solid s and Catalan Solid s from regular seeds. Applied in series these operators, it allows many higher order polyhedra. OPERATIONS ON POLYHEDRA
Some frequent combinations of operators have a shorter alternate notation:
The operators are applied like functions from right to left. For example:
All operations are ''symmetry-preserving'' except twisting ones like s and '''g''' which lose reflection symmetry. EXAMPLES The Cube can generate all the convex Octahedral Symmetry Uniform Polyhedra . The first row generates the Archimedean Solid s and the second row the Catalan Solid s, the second row forms being duals of the first. Comparing each new Polyhedron with the cube, each operation can be visually understood. (Two polyhedron forms don't have single operator names given by Conway.) GENERATING REGULAR SEEDS All of the five regular polyhedra can be generated from prismatic generators with zero to two operators:
EXTENSIONS TO CONWAY'S SYMBOLS The above operations allow all of the Semiregular Polyhedron s and Catalan Solid s to be generated from Regular Polyhedron s. Combined many higher operations can be made, but many interesting higher order polyhedra require new operators to be constructed. For example, geometric artist George W. Hart create an operation he called a ''propellor'', and another ''reflect'' to create mirror images of the rotated forms.
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