# Green's rules

Green's rules are a procedure for generating n -n -3 acrohedra. The rules are based off of Mason Green's construction of a 7-7-3 acrohedron, the small supersemicupola.

Green's Rules has produced valid n -n -3 acrohedra for n  = 4, 5, 6, 7, 8, 10, 5/2, 7/2, 8/3, and 10/3. All are orbiform.

## Procedure

The procedure can be described as follows:

2. Attach an n -gon to each edge.
3. Connect the second open edge of each new n -gon to the second open edge of n -gon attached to the virtual n -gon two edges away.
4. Add triangles to the triangular holes.
5. If the remaining open edges can be closed with a regular polygon or regular polygon compound close it, otherwise add n  n -gons and return to step 3.

### Example

The following is an example of Green's rules applied where n  = 10. The result is the gyrated blend of truncated dodecahedra.

## Examples

The following table shows the results of Green's rule for small n . For even n  Green's rule will result in a gyrated blend of .

Polyhedra generated by Green's rules
Acron Name Picture Notes
3-3-3 Generates a degenerate polyhedron topologically equivalent to a triangular bipyramid.
4-4-3 Gyrated blend of triangular prisms (tutrip)