SSCN (InstanceTopic, 3)

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Revision as of 12:52, 17 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
_n - scale by n, use brackets or subscripts if necessary

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

@@ Line 16: / Line 16: @@
 *Mx - transformation with [[matrix]] x
 *′ - [[invert]]
+*_n - scale by ''n'', use brackets or subscripts if necessary
 === Products ===