SSCN (InstanceTopic, 3)

From Hi.gher. Space

Revision as of 18:33, 19 November 2007

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