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 773 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.

Attach a decagon to each edge.

Fill the holes with triangles.

The shape cannot be closed so we add more decagons.

Fill the holes with triangles. The shape is now closed.
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 

333  Generates a degenerate polyhedron topologically equivalent to a triangular bipyramid.  
443  Gyrated blend of triangular prisms (tutrip)  
553  Great dodecahedral cone (gadcone)  
663  Gyrated blend of truncated tetrahedra (tutut)  
773  Small supersemicupola  
883  Gyrated blend of truncated cubes (tutic)  
993  Procedure does not generate a solution.  
10103  Gyrated blend of truncated dodecahedra (tutid)  
11113  Procedure does not generate a solution.  
12123  Gyrated blend of truncated hexagonal tilings  The 12123 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. "nn3 acrohedra".
 Klitzing, Richard. "Supersemicupola".