Toratopic notation (InstanceTopic, 3)
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'''Toratopic notation''' is a notation developed to represent [[toratope]]s. 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. | '''Toratopic notation''' is a notation developed to represent [[toratope]]s. 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). | + | 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. |
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[[Category:Geometric notation]] | [[Category:Geometric notation]] | ||
Revision as of 08:18, 2 December 2009
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.
