# SSCN (InstanceTopic, 3)

### From Higher Dimensions Database

**SSCN**, standing for **Standard Shape Construction Notation**, is a notation for defining shapes. It uses *operations*, in a similar but more flexible manner to CSG notation.

Note that SSCN is now obsolete. SSC2 provides a newer notation (advantages are listed on its page). This page concerns SSCN only, and should be used only for archaic reference.

## 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
- ′(ASCII: ') - invert

### Products

- () - Circular product
- [] - Square product (aka Cartesian product)
- <> - Tegmal 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
- {G5
^{3}}: Dodecahedron - [G3
^{2}]: Duoprism with*m*=*n*= 3 - [xy]^<xy>: Large hexadecachoron