Tapertopic notation (InstanceTopic, 3)
From Hi.gher. Space
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'''Tapertopic notation''' is a notation developed to represent [[tapertope]]s. Each digit represents a [[hypersphere]], square brackets represent a [[Cartesian product]], and a superscript ''n'' indicates ''n'' consecutive [[taper]]ings. Unlike [[rotopic digit and group notations]], superscripts apply only to the group or digit immediately preceding them, not to the entire string up to that point. This simplifies the necessary groupings and enables the string to be rearranged in any order. | '''Tapertopic notation''' is a notation developed to represent [[tapertope]]s. Each digit represents a [[hypersphere]], square brackets represent a [[Cartesian product]], and a superscript ''n'' indicates ''n'' consecutive [[taper]]ings. Unlike [[rotopic digit and group notations]], superscripts apply only to the group or digit immediately preceding them, not to the entire string up to that point. This simplifies the necessary groupings and enables the string to be rearranged in any order. | ||
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*If all of a sequence's digits are greater than one, then it will always roll when placed on a surface. | *If all of a sequence's digits are greater than one, then it will always roll when placed on a surface. | ||
*If it only has 1s then it only has flat sides and is incapable of rolling. | *If it only has 1s then it only has flat sides and is incapable of rolling. | ||
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Latest revision as of 21:11, 8 February 2014
Tapertopic notation is a notation developed to represent tapertopes. Each digit represents a hypersphere, square brackets represent a Cartesian product, and a superscript n indicates n consecutive taperings. Unlike rotopic digit and group notations, superscripts apply only to the group or digit immediately preceding them, not to the entire string up to that point. This simplifies the necessary groupings and enables the string to be rearranged in any order.
In common with rotopic digit notation, the sum of the numbers in a shape's notation is equal to the shape's dimensionality. All rotatopes have the same string for their tapertopic notation and rotopic digit notation.
Tapertopic notation also shows a useful property about the shapes: rolling.
- If a shape's tapertopic notation contains a non-superscript digit greater than 1, it is capable of rolling.
- If all of a sequence's digits are greater than one, then it will always roll when placed on a surface.
- If it only has 1s then it only has flat sides and is incapable of rolling.
