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 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)  Nonconvex conjugate: stelladodecahedron cone (5/25/23)  
663  Gyrated blend of truncated tetrahedra (tutut)  
773  Small supersemicupola  Nonconvex conjugate: great supersemicupola (7/27/23)  
883  Gyrated blend of truncated cubes (tutic)  Nonconvex conjugate: gyrated blend of quasitruncated hexahedra (8/38/33)  
993  Procedure does not generate a solution.  
10103  Gyrated blend of truncated dodecahedra (tutid)  Nonconvex conjugate: gyrated blend of quasitruncated small stellated dodecahedra (10/310/33)  
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.
Nonconvex conjugate: gyrated blend of quasitruncated hexagonal tilings (12/512/53) 
For n > 12 the n n 3 acron is hyperbolic.
External links[edit  edit source]
 McNeil, Jim. "nn3 acrohedra".
 Klitzing, Richard. "Supersemicupola".