Other than the prisms and anti-prisms, the only known solutions are for 7-4-3, 7-6-4, 7-7-3, 9-4-3, 11-4-3 and 7-3-4-3, the first three being imaged above.
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
N-6-4
N<=12 see 7-6-4
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 (no known solutions)
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