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