# Green's rules

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**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[edit | edit source]

The procedure can be described as follows:

- Start with a virtual n-gon.
- Attach an n-gon to each edge.
- 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.
- Add triangles to the triangular holes.
- 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[edit | edit source]

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

Start with a virtual decagon.

## Examples[edit | edit source]

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 .

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) | ||

5-5-3 | Great dodecahedral cone (gadcone) | ||

6-6-3 | Gyrated blend of truncated tetrahedra (tutut) | ||

7-7-3 | Small supersemicupola | ||

8-8-3 | Gyrated blend of truncated cubes (tutic) | ||

9-9-3 | Procedure does not generate a solution. | ||

10-10-3 | Gyrated blend of truncated dodecahedra (tutid) | ||

11-11-3 | Procedure does not generate a solution. | ||

12-12-3 | Gyrated blend of truncated hexagonal tiling | The 12-12-3 acron is planar and Green's rules result in a tiling of the plane. |

For n > 12 the n-n-3 acron is hyperbolic.

## External links[edit | edit source]

- McNeil, Jim. "n-n-3 acrohedra".
- Klitzing, Richard. "Supersemicupola".