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 degrees to five decimal places. I believe them to be accurate to +/- 0.00001 degrees)
Alternative versions of this page are available showing the dihedral angles in dd-mm-ss form and in radians.
The decimal degree data is also available in comma separated variable format
1. Acrons Found in Uniform Polyhedra
Acron
Dihedral Angles (Degrees)
A-B-C
A-B B-C
C-A
3-3-3
70.52878 70.52878 70.52878
4-4-3
60 90
90
4-4-4
90 90
90
5-4-4
90 108
90
5-5-5
116.56505 116.56505 116.56505
6-4-4
90 120
90
6-6-3
70.52878 109.47122 109.47122
6-6-4
109.47122 125.26439 125.26439
6-6-5
138.18969 142.62263 142.62263
8-4-4
90 135
90
8-6-4
125.26439 144.73561 135
8-8-3
90 125.26439 125.26439
10-4-4
90 144
90
10-6-4
142.62263 159.09484 148.28253
10-10-3
116.56505 142.62263 142.62263
2. Acrons Found In Johnson Solids
Acron
Dihedral Angles (Degrees)
A-B-C
A-B B-C
C-A
4-3-3
54.73561 109.47122 54.73561
5-3-3
37.37737 138.18969 37.37737
5-5-3
63.43495 100.81232 100.81232
6-4-3
54.73561 125.26439 70.52878
8-4-3
45 144.73561 54.73561
10-4-3
31.71747 159.09484 37.37737
10-5-3
63.43495 142.62263 79.18768
10-5-4
116.56505 148.28253 121.71747
3. Polydronic Acrons Not Found In Uniform Polyhedra or Johnson Solids
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 precise correlation between the solved acrons and those with a dihedral angle occurring in the above polyhedra.
Where a dihedral angle is shared between either two unsolved acrons, then this is noted.
Acron
Dihedral Angles (Degrees)
A-B-C
A-B B-C
C-A Shared angles with
5-4-3
58.28253 110.90516 79.18768
5-5-4
96.06017 108.96071 108.96071 5-5-4
= 8-5-4
6-5-3
65.19890 114.80110 94.51323 6-5-3
= 15-5-3
6-5-4
100.81232 121.71747
110.90516
6-5-5
124.24809 131.17486 124.24809 6-5-5
= 12-5-4
8-5-3
65.25526 132.13833 85.82933
8-5-4
108.96071 138.03008 115.91365 8-5-4
= 5-5-4
8-5-5
141.66758 152.53973 141.66758 8-5-5
= 16-5-4
8-6-3
76.16384 127.55160 103.83616
10-6-3
79.18768 138.18969
100.81232
10-8-3
99.9844 138.05347 126.47361
4. Apolydronic Acrons
Turning finally to apolydronic acrons (with an artificial upper limit of a pentadecagon), we see only a few have been resolved. None of the angles involved in these occur in the polydronic acrons.
Acron
Dihedral Angles (Degrees)
A-B-C
A-B B-C
C-A Shared angles with
7-4-3
50.24367 136.04986 62.58569 7-4-3
= 7-6-4
9-4-3
38.93477 152.19643 46.52332 9-4-3
= 9-6-4
11-4-3
22.35750 166.26298 26.05477 11-4-3
= 11-6-4
7-5-3
65.58640 124.7085 89.76916
9-5-3
64.49003 137.94314 82.36033
11-5-3
62.17081 146.49043 76.20928
12-5-3
60.74583 149.7539 73.36009
13-5-3
59.18983 152.5559 70.59566
14-5-3
57.52145 154.99833 67.88362
15-5-3
55.75191 157.15596 65.19890 15-5-3
= 6-5-3
16-5-3
53.88726 159.08513 62.52085
17-5-3
51.92953 160.8293 59.83133
18-5-3
49.87739 162.42279 57.11335
19-5-3
47.72632 163.89334 54.34991
20-5-3
45.46847 165.26399 51.52297
21-5-3
43.09215 166.55447 48.61217
22-5-3
40.58078 167.78241 45.59331
23-5-3
37.91107 168.96442 42.43602
24-5-3
35.04990 170.11732 39.10005
25-5-3
31.94850 171.25983 35.52881
26-5-3
28.53095 172.41550 31.63661
27-5-3
24.66831 173.61891 27.28028
28-5-3
20.10772 174.93222 22.18145
29-5-3
14.19374 176.51051 15.62123
7-5-4
105.01754 130.96334 113.28142
9-5-4
112.78189 143.65536 118.73408
11-5-4
120.37019 152.19574 124.86016 11-5-4
= 8-5-5
12-5-4
124.24809 155.58743 128.17271 12-5-4
= 6-5-5
13-5-4
128.24918 158.59494 131.67838
14-5-4
132.43107 161.32225 135.41514 14-5-4
= 7-5-5
15-5-4
136.86809 163.85448 139.44191
16-5-4
141.66758 166.26987 143.85242 16-5-4
= 8-5-5
17-5-4
147.00461 168.65467 148.80728
18-5-4
153.21572 171.13392 154.62271 18-5-4
= 9-5-5
19-5-4
161.16616 173.98314 162.11999
7-5-5
132.43107 142.64451 132.43107 7-5-5
= 14-5-4
9-5-5
153.21572 162.26785 153.21572 9-5-5
= 18-5-4
7-6-3
73.85690 119.86687 106.14310
9-6-3
77.86954 133.47668 102.13046 9-6-3
= 9-6-4 = 9-9-3 , 9-6-3 = 9-9-3
11-6-3
80.23978 142.03047 99.76022
12-6-3
81.10057 145.22189 98.89943
13-6-3
81.81881 147.91648 98.18119
14-6-3
82.42774 150.22226 97.57226
15-6-3
82.95092 152.21798 97.04908
16-6-3
83.40548 153.96238 96.59452
17-6-3
83.80426 155.50024 96.19574
18-6-3
84.15703 156.86624 95.84297
19-6-3
84.47139 158.08772 95.52861
20-6-3
84.75336 159.18651 95.24664
21-6-3
85.00772 160.18021 94.99228
22-6-3
85.23837 161.08325 94.76163
23-6-3
85.44851 161.90750 94.55149
24-6-3
85.64077 162.66285 94.35923
25-6-3
85.81734 163.35760 94.18266
26-6-3
85.98010 163.99877 94.01990
27-6-3
86.13059 164.59233 93.86941
28-6-3
86.27018 165.14339 93.72982
29-6-3
86.39999 165.65638 93.60001
30-6-3
86.52104 166.13510 93.47896
31-6-3
86.63418 166.58288 93.36582
32-6-3
86.74017 167.00263 93.25983
33-6-3
86.83967 167.39689 93.16033
34-6-3
86.93325 167.76793 93.06675
35-6-3
87.02143 168.11774 92.97857
36-6-3
87.10467 168.44809 92.89533
37-6-3
87.18337 168.76056 92.81663
38-6-3
87.25789 169.05656 92.74211
39-6-3
87.32856 169.33737 92.67144
40-6-3
87.39567 169.60412 92.60433
41-6-3
87.45949 169.85785 92.54051
42-6-3
87.52024 170.09948 92.47976
43-6-3
87.57815 170.32986 92.42185
44-6-3
87.63342 170.54977 92.36658
45-6-3
87.68621 170.75989 92.31379
46-6-3
87.73670 170.96087 92.26330
47-6-3
87.78502 171.15328 92.21498
48-6-3
87.83132 171.33768 92.16868
49-6-3
87.87572 171.51454 92.12428
50-6-3
87.91834 171.68433 92.08166
... etc
7-6-4
117.41431 136.04986 129.75633
7-6-4
= 7-7-3 =
14-7-3 , 7-6-4 = 7-4-3
9-6-4
133.47668 152.19643 141.06523
9-6-4
= 9-6-3 = 9-9-3 , 9-6-4 = 9-4-3
11-6-4
153.94523 166.26298 157.64250
11-6-4 = 11-11-3 , 11-6-4 = 11-4-3
7-6-5 156.46468 160.83663 158.67776
7-7-3
79.51267 117.41431 117.41431
7-7-3 = 7-6-4
= 14-7-3
8-7-3
83.86047 125.72651 116.15521
9-7-3
87.44772 132.14143 115.59295
10-7-3
90.55032 137.25906 115.47946
11-7-3
93.32461 141.44779 115.67557
12-7-3
95.86682 144.94754 116.09674
13-7-3
98.23994 147.92179 116.68852
14-7-3
100.48733 150.48598 117.41431
14-7-3 = 7-7-3 = 7-6-4
15-7-3
102.64004 152.72406 118.24870
16-7-3
104.72111 154.69863 119.17361
17-7-3
106.74823 156.45735 120.17599
18-7-3
108.73533 158.03721 121.24634
19-7-3
110.69377 159.46735 122.37774
20-7-3
112.63304 160.77112 123.56525
21-7-3
114.56130 161.96742 124.80545
22-7-3
116.48583 163.07180 126.09615
23-7-3
118.41329 164.09718 127.43621
24-7-3
120.34995 165.05442 128.82542
25-7-3
122.30198 165.95275 130.26442
26-7-3
124.27556 166.80013 131.75468
27-7-3
126.27711 167.60351 133.29853
28-7-3
128.31354 168.36907 134.89924
29-7-3
130.39240 169.10234 136.56114
30-7-3
132.52227 169.80846 138.28982
31-7-3
134.71311 170.49228 140.09242
32-7-3
136.97681 171.15853 141.97811
33-7-3
139.32793 171.81202 143.95868
34-7-3
141.78491 172.45787 146.04964
35-7-3
144.37185 173.10188 148.27180
36-7-3
147.12158 173.75101 150.65402
37-7-3
150.08109 174.41437 153.23812
38-7-3
153.32231 175.10498 156.08865
39-7-3
156.96616 175.84386 159.31466
40-7-3
161.24847 176.67109 163.12933
41-7-3
166.77900 177.68961 168.08426
7-7-4
129.49150 142.8895 142.88950
9-7-4
161.87715 168.4664 165.92493
9-8-3
95.26088 132.34514 125.60430
11-8-3
104.36661 142.78873 127.72440
12-8-3
108.53218 146.81036 129.27130
13-8-3
112.56773 150.29559 131.06415
14-8-3
116.53898 153.37078 133.07479
15-8-3
120.50069 156.12961 135.29052
16-8-3
124.50336 158.64446 137.71111
17-8-3
128.59881 160.97396 140.34827
18-8-3
132.84642 163.16868 143.22756
19-8-3
137.32188 165.27633 146.39351
20-8-3
142.13302 167.34804 149.92121
21-8-3
147.45373 169.44940 153.94337
22-8-3
153.61603 171.68787 158.72538
23-8-3
161.47047 174.31820 164.96096
9-9-3
102.13046 133.47668 133.47668 9-9-3
= 9-6-3 = 9-6-4 , 9-9-3 = 9-6-3
10-9-3
108.47739 139.92968 135.25405
11-9-3
114.55882 145.40284 137.53951
12-9-3
120.56090 150.18837 140.27348
13-9-3
126.64670 154.49792 143.45085
14-9-3
132.99331 158.50301 147.11943
15-9-3
139.84265 162.36946 151.40246
16-9-3
147.61804 166.31073 156.57752
17-9-3
157.36421 170.76175 163.40155
11-10-3
124.63037 149.09086 146.04985
12-10-3
133.05200 155.04605 150.26685
13-10-3
142.37566 160.87717 155.52201
14-10-3
153.83611 167.23730 162.58604
11-11-3
135.28500 153.94523 153.94523 11-11-3
= 11-6-4
12-11-3
147.72198 162.04191 160.52582
13-11-3
167.08561 173.11188 171.97975