SSCN (InstanceTopic, 3)

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Revision as of 17:16, 26 October 2008

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 to the specified Dx number
D - dual
A - alternation
P - pyramid
T - hypertorus
Wx - hypertorus with 1/x twist
Cx - convex hull with net space x
Mx - transformation with matrix x
′ - invert

Products

() - Circular product
[] - Square product (aka Cartesian product)
<> - Tegal product
∩ (ASCII: n) - intersection
∪ (ASCII: u) - 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
xW2: Möbius strip
[xyz]X2D: Rhombic dodecahedron
<xyz>X7A: Cubic snub
G4P: Square pyramid
(xy)T: Torus
{G5³}: Dodecahedron
[G3²]: Duoprism with m = n = 3
[xy]^<xy>: Large hexadecachoron

@@ Line 21: / Line 21: @@
 *[] - [[Square product]] (aka [[Cartesian product]])
 *<> - [[Tegal product]]
-*∩ - [[intersection]]
+*∩ (ASCII: n) - [[intersection]]
-*∪ - [[union]]
+*∪ (ASCII: u) - [[union]]
 === Miscellaneous ===