SSCN (InstanceTopic, 3)
From Hi.gher. Space
Standard Shape Construction notation, abbreviated as SSC notation, is a notation for defining shapes. It uses operations, in a similar but more flexible manner to CSG notation.
Operations
Creation
- Gx - start new group, regular polygon with x vertices
- Rx - recall saved group x (saved groups are numbered from 0 upwards from left to right)
Single
- Xx - truncate x-cells (in binary: 0 does nothing, 1 = t0, 2 = t1, 3 = t0,1, 4 = t2, etc etc.
- Wx - perform a 1/x twist along the xz plane (rename dimensions or use transformations to change its effect)
- D - dual
- A - alternation
- P - pyramid
- T - hypertorus
- Cx - convex hull with net space x
- Mx - transformation with matrix x
- ′ - invert
Products
- () - Circular product
- [] - Square product (aka Cartesian product)
- <> - Tegal product
- ∩ - intersection
- ∪ - union
Miscellaneous
- {} - vertex layout fold
- ^n - powertope, where n is a group, or multiple copies of the shape, where n is an integer (can also use superscript)
- S - save group to use with Rx
Notes
- All groups that aren't products must begin with either Gx or Rx.
- Dimensions may be specified immediately before a group by using lowercase letters.
- Lowercase letters with no group after them indicate a line segment in that dimension.
- Tigroids are not representable in this notation unless they can be well defined without using spheration.
- Any bracketope's bracket notation can also be used as its SSCN.
Examples
- G3: Triangle
- [xyz]X3: Cubic truncate
- G4W2T: Möbius strip
- [xyz]X2D: Rhombic dodecahedron
- <xyz>X7A: Cubic snub
- G4P: Square pyramid
- [(xy)z]T: Torus
- {G53}: Dodecahedron
- [G32]: Duoprism with m = n = 3
- [xy]^<xy>: Large hexadecachoron