Bowers' rotatope notation

Bowers' Rotatope Notation is a notation created by Jonathan Bowers to represent rotatopes.

In the notation, a line segment is represented as $$|$$ and an n-dimensional hypersphere is represented as $$({ | }^{ n-2 })$$ (for example, a circle is $$$$ and a glome is $$(||)$$).

Two of these elements placed adjacent to each other represent the multiplication of the two polytopes.

Strings in rotatope notation have the interesting property that they are the same length as the dimension of the rotatope they represent; for example, $$(||||)|$$represents a seven-dimensional Hexaphere-Based Prism, and is seven characters long.

Since there are only two states for the entries - a bracket or a line - strings in rototope notation can be stored using a maximum of one bit per dimension. An example encoding would be to have 0 for brackets and 1 for lines. This would make a Hexaphere-Based Prism representable using 0111101.