Schläfli symbol (InstanceTopic, 3)

From Higher Dimensions Database

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 hypercell of dimension 0 for the 2nd number and increasing by one for every number, 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 {4,3,3} 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. {4,3,3} is therefore a tesseract because a tesseract has three cubes attached to each of its sides.