It is fascinating to look at the dihedral angles in trihedral acrons and compare those acrons which have been resolved with those that have not.
We begin by looking at Uniform Polyhedra and Johnson Solids:
(note: all dihedral angles are presented in radians to six decimal places. I believe them to be accurate to +/- 0.000001 radians)
Alternative versions of this page are available showing the dihedral angles in decimal degrees and in dd-mm-ss form.
The decimal degree data is also available in comma separated variable format
1. Acrons Found in Uniform Polyhedra
Acron
Dihedral Angles (Radians)
A-B-C
A-B B-C
C-A
3-3-3
1.230959 1.230959
1.230959
4-4-3
1.047198 1.570796
1.570796
4-4-4
1.570796 1.570796
1.570796
5-4-4
1.570796 1.884956
1.570796
5-5-5
2.034444 2.034444
2.034444
6-4-4
1.570796 2.094395
1.570796
6-6-3
1.230959 1.910633
1.910633
6-6-4
1.910633 2.186276
2.186276
6-6-5
2.411865 2.489235
2.489235
8-4-4
1.570796 2.356194
1.570796
8-6-4
2.186276 2.526113
2.356194
8-8-3
1.570796 2.186276
2.186276
10-4-4
1.570796 2.513274
1.570796
10-6-4
2.489235 2.776729
2.588018
10-10-3
2.034444 2.489235
2.489235
2. Acrons Found In Johnson Solids
Acron
Dihedral Angles (Radians)
A-B-C
A-B B-C
C-A
4-3-3
0.955317 1.910633
0.955317
5-3-3
0.652358 2.411865
0.652358
5-5-3
1.107149 1.759507
1.759507
6-4-3
0.955317 2.186276
1.230959
8-4-3
0.785398 2.526113
0.955317
10-4-3
0.553574 2.776729
0.652358
10-5-3
1.107149 2.489235
1.382086
10-5-4
2.034444 2.588018
2.124371
Looking now at the remaining polydronic acrons, we can colour code the acrons themselves: green if resolved, black otherwise. We can also colour code the dihedral angles: red if they occur in a Uniform Polyhedron, blue if they occur in a Johnson Solid and black otherwise. Note the exact correlation between those acrons which have been resolved and those with dihedral angles occurring in the above polyhedra.
3. Polydronic Acrons
Not Found In Uniform Polyhedra or Johnson Solids
Acron
Dihedral Angles (Radians)
A-B-C
A-B B-C
C-A
5-4-3
1.017222 1.935660 1.382086
5-5-4
1.676566 1.901723 1.901723
6-5-3
1.137935 2.003657 1.649567
6-5-4
1.759507 2.124371
1.935660
6-5-5
2.168538 2.289433 2.168538
8-5-3
1.138919 2.306249 1.498004
8-5-4
1.901723 2.409079 2.023075
8-5-5
2.472566 2.662321 2.472566
8-6-3
1.329310 2.226195 1.812283
10-6-3
1.382086 2.411865
1.759507
10-8-3
1.745057 2.409488 2.207381
Turning finally to apolydronic acrons (with an artificial upper limit of a pentadecagon), we see only the first three have been resolved although the angles do not occur in the polydronic acrons. I believe this to be a feature of the precise solutions found to these acrons where angles are 'cancelled out' by connecting two identical polyhedral sections. This implies that solutions may exist to the outstanding acrons above although I believe such solutions will be 'paired solutions' in similar fashion to the resolved apolydronic acrons.
4. Apolydronic Acrons
Acron
Dihedral Angles (Radians)
A-B-C
A-B B-C
C-A
7-4-3
0.876917 2.374518 1.092326
9-4-3
0.679540 2.656329 0.811985
11-4-3
0.390212 2.901836 0.454742
7-5-3
1.144699 2.176574 1.566767
9-5-3
1.125563 2.407562 1.437459
11-5-3
1.085085 2.556740 1.330103
12-5-3
1.060215 2.613699 1.280375
13-5-3
1.033057 2.662603 1.232127
14-5-3
1.003939 2.705231 1.184793
15-5-3
0.973054 2.742889 1.137935
16-5-3
0.940510 2.776559 1.091195
17-5-3
0.906341 2.807001 1.044254
18-5-3
0.870525 2.834813 0.996816
19-5-3
0.832981 2.860478 0.948585
20-5-3
0.793575 2.884401 0.899245
21-5-3
0.752100 2.906924 0.848442
22-5-3
0.708268 2.928355 0.795753
23-5-3
0.661673 2.948985 0.740648
24-5-3
0.611736 2.969107 0.682425
25-5-3
0.557606 2.989048 0.620095
26-5-3
0.497959 3.009218 0.552163
27-5-3
0.430543 3.030222 0.476131
28-5-3
0.350946 3.053143 0.387139
29-5-3
0.247727 3.080690 0.272642
7-5-4
1.832902 2.285741 1.977134
9-5-4
1.968415 2.507259 2.072301
11-5-4
2.100856 2.656317 2.179221
12-5-4
2.168538 2.715513 2.237036
13-5-4
2.238371 2.768004 2.298221
14-5-4
2.311358 2.815604 2.363440
15-5-4
2.388799 2.859800 2.433720
16-5-4
2.472566 2.901957 2.510698
17-5-4
2.565715 2.943579 2.597177
18-5-4
2.674119 2.986850 2.698675
19-5-4
2.812880 3.036579 2.829528
7-5-5
2.311358 2.489616 2.311358
9-5-5
2.674119 2.832108 2.674119
7-6-3
1.289046 2.092072 1.852546
9-6-3
1.359080 2.329608 1.782513
11-6-3
1.400448 2.478899 1.741144
12-6-3
1.415472 2.534600 1.726121
13-6-3
1.428008 2.581630 1.713585
14-6-3
1.438636 2.621873 1.702957
15-6-3
1.447767 2.656705 1.693826
16-6-3
1.455700 2.687151 1.685892
17-6-3
1.462660 2.713991 1.678932
18-6-3
1.468817 2.737832 1.672775
19-6-3
1.474304 2.759151 1.667289
20-6-3
1.479225 2.778329 1.662368
21-6-3
1.483665 2.795672 1.657928
22-6-3
1.487690 2.811433 1.653902
23-6-3
1.491358 2.825819 1.650235
24-6-3
1.494713 2.839002 1.646879
25-6-3
1.497795 2.851128 1.643797
26-6-3
1.500636 2.862318 1.640957
27-6-3
1.503262 2.872678 1.63833
28-6-3
1.505699 2.882296 1.635894
29-6-3
1.507964 2.891249 1.633628
30-6-3
1.510077 2.899605 1.631516
31-6-3
1.512052 2.907420 1.629541
32-6-3
1.513902 2.914746 1.627691
33-6-3
1.515638 2.921627 1.625955
34-6-3
1.517271 2.928103 1.624321
35-6-3
1.518810 2.934208 1.622782
36-6-3
1.520263 2.939974 1.621329
37-6-3
1.521637 2.945427 1.619956
38-6-3
1.522937 2.950594 1.618655
39-6-3
1.524171 2.955495 1.617422
40-6-3
1.525342 2.960150 1.616250
41-6-3
1.526456 2.964579 1.615137
42-6-3
1.527516 2.968796 1.614076
43-6-3
1.528527 2.972817 1.613066
44-6-3
1.529492 2.976655 1.612101
45-6-3
1.530413 2.980322 1.611180
46-6-3
1.531294 2.983830 1.610298
47-6-3
1.532138 2.987188 1.609455
48-6-3
1.532946 2.990407 1.608647
49-6-3
1.533721 2.993494 1.607872
50-6-3
1.534465 2.996457 1.607128
7-6-4
2.049266 2.374518 2.264675
9-6-4
2.329608 2.656329 2.462053
11-6-4
2.686851 2.901836 2.751381
7-6-5
2.730824 2.807129 2.769449
7-7-3
1.387758 2.049266 2.049266
8-7-3
1.463641 2.194342 2.027291
9-7-3
1.526251 2.306303 2.017478
10-7-3
1.580401 2.395622 2.015497
11-7-3
1.628822 2.468730 2.018920
12-7-3
1.673192 2.529812 2.026270
13-7-3
1.714610 2.581722 2.036599
14-7-3
1.753835 2.626476 2.049266
15-7-3
1.791407 2.665538 2.063829
16-7-3
1.827728 2.700000 2.079972
17-7-3
1.863108 2.730696 2.097467
18-7-3
1.897790 2.758270 2.116148
19-7-3
1.931971 2.783230 2.135895
20-7-3
1.965817 2.805985 2.156621
21-7-3
1.999472 2.826865 2.178266
22-7-3
2.033061 2.846140 2.200793
23-7-3
2.066702 2.864036 2.224181
24-7-3
2.100503 2.880743 2.248428
25-7-3
2.134572 2.896422 2.273543
26-7-3
2.169018 2.911211 2.299553
27-7-3
2.203951 2.925233 2.326498
28-7-3
2.239494 2.938595 2.354436
29-7-3
2.275777 2.951393 2.383442
30-7-3
2.312950 2.963717 2.413613
31-7-3
2.351187 2.975652 2.445074
32-7-3
2.390696 2.987280 2.477985
33-7-3
2.431731 2.998685 2.512553
34-7-3
2.474613 3.009958 2.549047
35-7-3
2.519764 3.021198 2.587831
36-7-3
2.567756 3.032527 2.629409
37-7-3
2.619409 3.044105 2.674510
38-7-3
2.675979 3.056158 2.724261
39-7-3
2.739576 3.069054 2.780565
40-7-3
2.814317 3.083492 2.847144
41-7-3
2.910843 3.101269 2.933624
7-7-4
2.260053 2.493892 2.493892
9-7-4
2.825289 2.940293 2.895936
9-8-3
1.662616 2.309859 2.192209
11-8-3
1.821541 2.492134 2.229211
12-8-3
1.894244 2.562324 2.256210
13-8-3
1.964677 2.623153 2.287501
14-8-3
2.033989 2.676825 2.322593
15-8-3
2.103134 2.724976 2.361265
16-8-3
2.172993 2.768868 2.403512
17-8-3
2.244473 2.809526 2.449539
18-8-3
2.318607 2.847831 2.499793
19-8-3
2.396719 2.884616 2.555049
20-8-3
2.480689 2.920774 2.616619
21-8-3
2.573553 2.95745 2.686819
22-8-3
2.681105 2.996519 2.770280
23-8-3
2.818191 3.042427 2.879112
9-9-3
1.782513 2.329608 2.329608
10-9-3
1.893288 2.442234 2.360629
11-9-3
1.999429 2.537758 2.400517
12-9-3
2.104185 2.621282 2.448234
13-9-3
2.210402 2.696497 2.503690
14-9-3
2.321171 2.766399 2.567718
15-9-3
2.440715 2.833882 2.642471
16-9-3
2.576421 2.902670 2.732793
17-9-3
2.746524 2.980355 2.851895
11-10-3
2.175210 2.602126 2.549051
12-10-3
2.322195 2.706064 2.622651
13-10-3
2.484924 2.807836 2.714371
14-10-3
2.684947 2.918841 2.837662
11-11-3
2.361169 2.686851 2.686851
12-11-3
2.578235 2.828165 2.801704
13-11-3
2.916194 3.021372 3.001613