Schläfli symbol (InstanceTopic, 3)
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A '''Schläfli symbol''' is a method of representing [[uniform polytope]]s. Schläfli symbols involve a list of numbers separated by commas and surrounded by braces. There must be at least one number in the list. | A '''Schläfli symbol''' is a method of representing [[uniform polytope]]s. Schläfli symbols involve a list of numbers separated by commas and surrounded by braces. There must be at least one number in the list. | ||
| - | For any shape with a Schläfli symbol, its dimension will be the number of numbers in the list plus one. The list of numbers is read from left to right. For the first number, create a [[regular | + | For any shape with a Schläfli symbol, its dimension will be the number of numbers in the list plus one. The list of numbers is read from left to right. For the first number, create a [[regular polygon]] with that number of sides. For every other number afterwards, tile the original shape that number to a [[vertex]], and then take the shape to be the [[hypervolume]] it previously bounded. |
Schläfli symbols can also be used to define shapes in [[hyperbolic space]]. | Schläfli symbols can also be used to define shapes in [[hyperbolic space]]. | ||
Revision as of 19:47, 17 August 2007
A Schläfli symbol is a method of representing uniform polytopes. Schläfli symbols involve a list of numbers separated by commas and surrounded by braces. There must be at least one number in the list.
For any shape with a Schläfli symbol, its dimension will be the number of numbers in the list plus one. The list of numbers is read from left to right. For the first number, create a regular polygon with that number of sides. For every other number afterwards, tile the original shape that number to a vertex, and then take the shape to be the hypervolume it previously bounded.
Schläfli symbols can also be used to define shapes in hyperbolic space.
For example, the shape {4,3,4} is a tesseract. {4} is a square because a square has four sides. {4,3} is therefore a cube because a cube has three squares attached to each of its vertices. {4,3,4} is therefore a tesseract because a tesseract has four cubes attached to each of its vertices.
