SSC2 (InstanceTopic, 3)

From Hi.gher. Space

SSC2, standing for Standard Shape Construction version 2, is a notation for defining shapes. It is the successor to SSCN (also known as SSC1 or just SSC). SSC2 is the newest and preferred method for writing the definition of a shape.

Scope

SSC2, like its predecessor, is concerned only with the structure of a shape, not its position, size, orientation or indeed stretching of any particular hypercell. Both versions do include a matrix transformation operation, but while the first version defined orientation either explicitly or implicitly, SSC2 includes this operation only so that boolean operations can become useful.

Fundamental sets

SSC2 has five articles called the fundamental sets. Each of these sets is infinite, but there are a finite number of shapes in each dimension in each set. Each set provides a method of enumeration which can later be used to enumerate any shape based on its SSC2 notation. Shapes are defined by referencing elements of the fundamental sets and combining them with various operators.

Manifolds

Manifolds are written in the form Mx, where x is the index of the manifold. This set is chosen to be the first in the list of sets because of all the SSC2 fundamental sets, it is the only one which contains the point and the line as the first two elements.

Regular polygons

Regular polygons are written in the form Gx, where x is the number of vertices in the polygon. G0, G1 and G2 are not valid.

Regular polygon duals

Regular polygon duals are exactly the same as regular polygons except they are written as Hx rather than Gx. Functionally, they are mainly used as brick products, for example the diamond, H4, is the tegal product.

Kanitopes

Kanitopes are written in one of two forms: Kfx for three- or four-dimensional shapes or Knfx for higher-dimensional shapes. Here, n is the shape's dimension, f is the family and x is the Dx number. Families are written with one letter, using t, o, i; p, e, k, s for Schlaefli symbols {3,3}, {3,4}, {3,5}; {3,3,3}, {3,3,4}, {3,4,3}, {3,3,5} respectively.

Toratopes

Toratopes are written in the form Tx. Here, x can either be an integer, in which case the toratope is an x-dimensional hypersphere, or a string in rotopic group notation restricted to having no superscripts and an outer pair of parentheses (thus making the string always represent a toratope, not just a more general rotope).

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