Rotopic group notation (EntityClass, 3)

From Hi.gher. Space

In group notation, letters are used to represent dimensions.

• A normal letter represents that the object is extruded in that dimension.
• A superscript letter represents that the object is tapered in that direction.
• A pair of parentheses represents that the object is spherated.

Conversions

To digit notation

1. Change every letter (subscript or not) to a number 1.
2. If there is a sequence (111...) with n 1s and nothing else inside the parentheses, change the entire sequence, including parentheses, to the number n.
3. If there is a sequence of superscript 1s, change the sequence to the number of 1s in the sequence, retaining the superscript.

To surface equation

Marek14 found a way to convert group notation to a surface equation, edited here for ease of use:

Using the example (((xy)z)w):

1. Make a square of each variable and add terms within parenthesis: (((x²+y²)+z²)+w²)
2. Replace each parenthesis with a square root function: sqrt(sqrt(sqrt(x²+y²)+z²)+w²)
3. Immediately outside of each square root function, subtract a parameter and square this: (sqrt((sqrt((sqrt(x²+y²)-A)²+z²)-B)²+w²)-C)²
4. Remove the outermost square and parentheses, and form an equation with this expression as the LHS and zero as the RHS: sqrt((sqrt((sqrt(x²+y²)-A)²+z²)-B)²+w²)-C = 0

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