Toratopic notation (InstanceTopic, 3)

From Higher Dimensions Database

Toratopic notation is a notation developed to represent toratopes. Each vertical line (written as the capital letter I) represents a digon and parentheses represent spheration. Unlike rotopic digit and group notations, superscripts are not allowed, which prevents ambiguous and immeasurable rotopes from forming and enables the string to be rearranged in any order.

The number of vertical lines in a shape's notation is equal to the shape's dimensionality. A common shorthand is to write 1 instead of a vertical line, and to replace any pair of brackets with the number of lines in it, as long as the brackets only contains lines and not other brackets. For example, ((II)II) is often written as (211). Using this shorthand for a rotatope will give its tapertopic notation. However, the normalized/canonical form of toratopic notation is to use vertical bars with largest groups first.