Apolydronic acrons

An apolydronic polygon is any polygon not occurring within the uniform polyhedra or Johnson Solids. So it is any (non-starred) polygon exclusing the triangle,  square, pentagon, hexagon, octagon and decagon.

Other than the prisms and anti-prisms, there are a number of acrons that have been discovered in recent years.

A full list of possible apolydronic acrons is as follows.  In all cases N should be taken as excluding the numbers 3,4,5,6,8 and 10 and being equal to or larger than the second number listed.

Trihedral apolydronic acrons

N-3-3      N<=6           no apolydronic candidates
N-4-3      N<=12         fully covered by 7-4-3, 9-4-3 and 11-4-3
N-4-4      all N            prisms
N-5-3      N<=30
N-5-4      N<=20
N-5-5      N=7 or N=9
N-6-3      all N           fully covered by Rayne H.'s n-6-3 acrohedra
N-6-4      N<=12        fully covered by 7-6-4 , 9-6-4 and 11-6-4
7-6-5
N-7-3      N<=42        see 7-7-3
N-7-4      N=7 or N=9
N-8-3      N<=24
N-9-3      N<=18
N-10-3    N<=15
N-11-3    N<=13

Tetrahedral apolydronic acrons

N-3-3-3   all N            antiprisms
N-3-4-3   N<=12        see 7-3-4-3
7-3-5-3
N-4-3-3   N<=12
7-5-3-3

Pentahedral apolydronic acrons

None