double_corner_types.txt

This is a list of Bram's sphere type twisty puzzle geometries that (potentially) have two or more 
corner types simultaneously. For details and notation, see the forum thread at 
http://twistypuzzles.com/forum/viewtopic.php?f=1&t=31829 

The list is divided into several sections. You will need to play around with the cut depths to get
these to work. So far, most of the ones I've tried have worked for me after a bit of fiddling. Note
that some of these are trivial, e.g. just related to the symmetries of the cube, but others are
quite unexpected.

In this list, sides can have up to 20 stops, and pieces with symmetries up to 8 are considered. 
Angles  are in degrees. I didn't consider anything beyond 4/n1, but I can easily generate those 
(or send Python code) if anyone is interested.

These all use the first version of will_57's formula, the one with the minus sign. I did try the other
formula as well, but its results all seem to be duplicates of the ones below, so I've left them out.


Part 1: puzzles where [1/n1, 1/n2, c] = [2/n1, 1/n1, d]

[1/3, 1/2: 1/5] = 159.09484255211072
[2/3, 1/2: 1/5] = 159.0948425521107

[1/3, 1/2: 1/4] = 144.73561031724537
[2/3, 1/2: 1/4] = 144.73561031724535

[1/3, 1/2: 2/7] = 136.04985798351382
[2/3, 1/2: 2/7] = 136.04985798351382

[1/3, 1/2: 1/3] = 125.26438968275468
[2/3, 1/2: 1/3] = 125.26438968275465

[1/3, 1/2: 3/8] = 116.22419854710421
[2/3, 1/2: 3/8] = 116.22419854710421

[1/3, 1/2: 2/5] = 110.90515744788931
[2/3, 1/2: 2/5] = 110.90515744788931

[1/3, 1/2: 3/7] = 104.88886866379032
[2/3, 1/2: 3/7] = 104.88886866379032

[1/3, 1/2: 4/7] = 75.11113133620968
[2/3, 1/2: 4/7] = 75.1111313362097

[1/3, 1/2: 3/5] = 69.09484255211069
[2/3, 1/2: 3/5] = 69.09484255211072

[1/3, 1/2: 5/8] = 63.775801452895784
[2/3, 1/2: 5/8] = 63.77580145289581

[1/3, 1/2: 2/3] = 54.73561031724535
[2/3, 1/2: 2/3] = 54.73561031724538

[1/3, 1/2: 5/7] = 43.95014201648621
[2/3, 1/2: 5/7] = 43.95014201648623

[1/3, 1/2: 3/4] = 35.264389682754654
[2/3, 1/2: 3/4] = 35.264389682754675

[1/3, 1/2: 4/5] = 20.905157447889305
[2/3, 1/2: 4/5] = 20.90515744788934

[1/3, 1/3: 1/5] = 138.1896851042214
[2/3, 1/3: 2/5] = 138.18968510422138

[1/3, 1/3: 1/3] = 109.47122063449069
[2/3, 1/3: 1/2] = 109.47122063449069

[1/3, 1/3: 1/2] = 70.52877936550931
[2/3, 1/3: 2/3] = 70.52877936550932

[1/3, 1/3: 3/5] = 41.81031489577859
[2/3, 1/3: 4/5] = 41.81031489577861

[1/3, 1/4: 1/4] = 125.26438968275465
[2/3, 1/4: 1/2] = 125.26438968275465

[1/3, 1/4: 1/2] = 54.735610317245346
[2/3, 1/4: 3/4] = 54.735610317245346

[1/3, 1/5: 1/5] = 142.62263185935032
[2/3, 1/5: 1/2] = 142.6226318593503

[1/3, 1/5: 1/3] = 100.81231696357172
[2/3, 1/5: 3/5] = 100.8123169635717

[1/3, 1/5: 2/5] = 79.18768303642828
[2/3, 1/5: 2/3] = 79.1876830364283

[1/3, 1/5: 1/2] = 37.37736814064968
[2/3, 1/5: 4/5] = 37.37736814064969

[1/4, 1/2: 1/3] = 135.00000000000003
[2/4, 1/2: 1/4] = 135.0

[1/4, 1/2: 2/3] = 45.000000000000014
[2/4, 1/2: 3/4] = 45.00000000000001

[1/4, 1/3: 1/4] = 125.26438968275465
[2/4, 1/3: 1/3] = 125.26438968275468

[1/4, 1/3: 1/2] = 54.735610317245346
[2/4, 1/3: 2/3] = 54.73561031724535

[1/4, 1/4: 1/3] = 90.0
[2/4, 1/4: 1/2] = 90.0

[1/5, 1/2: 1/3] = 148.28252558853902
[2/5, 1/2: 1/5] = 148.282525588539

[1/5, 1/2: 2/5] = 121.717474411461
[2/5, 1/2: 1/3] = 121.717474411461

[1/5, 1/2: 3/5] = 58.282525588538995
[2/5, 1/2: 2/3] = 58.28252558853901

[1/5, 1/2: 2/3] = 31.717474411461037
[2/5, 1/2: 4/5] = 31.71747441146101

[1/5, 1/3: 1/5] = 142.62263185935032
[2/5, 1/3: 1/5] = 142.62263185935032

[1/5, 1/3: 1/3] = 100.81231696357172
[2/5, 1/3: 2/5] = 100.81231696357172

[1/5, 1/3: 2/5] = 79.18768303642828
[2/5, 1/3: 1/2] = 79.18768303642828

[1/5, 1/3: 1/2] = 37.37736814064968
[2/5, 1/3: 2/3] = 37.377368140649715

[1/5, 1/5: 1/5] = 116.56505117707799
[2/5, 1/5: 1/3] = 116.56505117707799

[1/5, 1/5: 1/3] = 63.43494882292203
[2/5, 1/5: 1/2] = 63.43494882292201

[1/7, 1/3: 2/7] = 117.4143079054384
[2/7, 1/3: 2/7] = 117.41430790543843



Part 2: puzzles where [2/n1, 1/n2, c] = [3/n1, 1/n1, d]

[2/4, 1/2: 1/4] = 135.0
[3/4, 1/2: 1/3] = 135.00000000000003

[2/4, 1/2: 3/4] = 45.00000000000001
[3/4, 1/2: 2/3] = 45.00000000000003

[2/4, 1/3: 1/3] = 125.26438968275468
[3/4, 1/3: 1/2] = 125.26438968275465

[2/4, 1/3: 2/3] = 54.73561031724535
[3/4, 1/3: 3/4] = 54.73561031724535

[2/4, 1/4: 1/2] = 90.0
[3/4, 1/4: 2/3] = 90.00000000000003

[2/5, 1/2: 1/8] = 166.26986711424698
[3/5, 1/2: 1/8] = 166.26986711424695

[2/5, 1/2: 1/7] = 161.32225322116653
[3/5, 1/2: 1/7] = 161.3222532211665

[2/5, 1/2: 1/6] = 155.5874284095368
[3/5, 1/2: 1/6] = 155.5874284095368

[2/5, 1/2: 1/5] = 148.282525588539
[3/5, 1/2: 1/5] = 148.282525588539

[2/5, 1/2: 1/4] = 138.03008476562457
[3/5, 1/2: 1/4] = 138.03008476562457

[2/5, 1/2: 2/7] = 130.96333778188585
[3/5, 1/2: 2/7] = 130.96333778188585

[2/5, 1/2: 1/3] = 121.717474411461
[3/5, 1/2: 1/3] = 121.717474411461

[2/5, 1/2: 3/8] = 113.72687139412194
[3/5, 1/2: 3/8] = 113.72687139412194

[2/5, 1/2: 2/5] = 108.96070988192251
[3/5, 1/2: 2/5] = 108.96070988192251

[2/5, 1/2: 3/7] = 103.53105443738653
[3/5, 1/2: 3/7] = 103.53105443738653

[2/5, 1/2: 4/7] = 76.46894556261347
[3/5, 1/2: 4/7] = 76.46894556261348

[2/5, 1/2: 3/5] = 71.03929011807749
[3/5, 1/2: 3/5] = 71.03929011807749

[2/5, 1/2: 5/8] = 66.27312860587807
[3/5, 1/2: 5/8] = 66.27312860587807

[2/5, 1/2: 2/3] = 58.28252558853901
[3/5, 1/2: 2/3] = 58.28252558853901

[2/5, 1/2: 5/7] = 49.036662218114174
[3/5, 1/2: 5/7] = 49.036662218114174

[2/5, 1/2: 3/4] = 41.96991523437545
[3/5, 1/2: 3/4] = 41.96991523437545

[2/5, 1/2: 4/5] = 31.71747441146101
[3/5, 1/2: 4/5] = 31.717474411461023

[2/5, 1/2: 5/6] = 24.412571590463177
[3/5, 1/2: 5/6] = 24.41257159046319

[2/5, 1/2: 6/7] = 18.67774677883351
[3/5, 1/2: 6/7] = 18.677746778833527

[2/5, 1/2: 7/8] = 13.730132885753038
[3/5, 1/2: 7/8] = 13.730132885753065

[2/5, 1/3: 1/5] = 142.62263185935032
[3/5, 1/3: 1/3] = 142.62263185935032

[2/5, 1/3: 2/5] = 100.81231696357172
[3/5, 1/3: 1/2] = 100.81231696357172

[2/5, 1/3: 1/2] = 79.18768303642828
[3/5, 1/3: 3/5] = 79.1876830364283

[2/5, 1/3: 2/3] = 37.377368140649715
[3/5, 1/3: 4/5] = 37.37736814064971

[2/5, 1/5: 1/3] = 116.56505117707799
[3/5, 1/5: 1/2] = 116.56505117707799

[2/5, 1/5: 1/2] = 63.43494882292201
[3/5, 1/5: 2/3] = 63.43494882292203

[2/7, 1/2: 1/3] = 129.75633481662646
[3/7, 1/2: 2/7] = 129.75633481662646

[2/7, 1/2: 2/3] = 50.24366518337357
[3/7, 1/2: 5/7] = 50.24366518337358

[2/7, 1/3: 2/7] = 117.41430790543843
[3/7, 1/3: 1/3] = 117.41430790543843

[2/7, 1/3: 3/7] = 82.42774243307761
[3/7, 1/3: 1/2] = 82.42774243307763

[2/8, 1/2: 3/8] = 122.76509973964892
[3/8, 1/2: 1/3] = 122.76509973964892

[2/8, 1/2: 5/8] = 57.2349002603511
[3/8, 1/2: 2/3] = 57.23490026035111

[2/8, 1/3: 1/3] = 103.83616047925648
[3/8, 1/3: 3/8] = 103.83616047925648


Part 2: puzzles where [2/n1, 1/n2, c] = [3/n1, 1/n1, d]  
(I have not tried any of these yet and don't know how well they work.)

[3/5, 1/2: 1/5] = 148.282525588539
[4/5, 1/2: 1/3] = 148.282525588539

[3/5, 1/2: 1/3] = 121.717474411461
[4/5, 1/2: 2/5] = 121.717474411461

[3/5, 1/2: 2/3] = 58.28252558853901
[4/5, 1/2: 3/5] = 58.28252558853902

[3/5, 1/2: 4/5] = 31.717474411461023
[4/5, 1/2: 2/3] = 31.717474411461072

[3/5, 1/3: 1/3] = 142.62263185935032
[4/5, 1/3: 1/2] = 142.62263185935032

[3/5, 1/3: 1/2] = 100.81231696357172
[4/5, 1/3: 3/5] = 100.81231696357172

[3/5, 1/3: 3/5] = 79.1876830364283
[4/5, 1/3: 2/3] = 79.18768303642833

[3/5, 1/3: 4/5] = 37.37736814064971
[4/5, 1/3: 4/5] = 37.37736814064974

[3/5, 1/5: 1/2] = 116.56505117707799
[4/5, 1/5: 2/3] = 116.56505117707802

[3/5, 1/5: 2/3] = 63.43494882292203
[4/5, 1/5: 4/5] = 63.43494882292202

[3/7, 1/2: 1/8] = 161.37673463176404
[4/7, 1/2: 1/8] = 161.37673463176404

[3/7, 1/2: 1/7] = 157.5388737692873
[4/7, 1/2: 1/7] = 157.5388737692873

[3/7, 1/2: 1/6] = 152.66000528300194
[4/7, 1/2: 1/6] = 152.66000528300194

[3/7, 1/2: 1/5] = 146.08049582135365
[4/7, 1/2: 1/5] = 146.08049582135365

[3/7, 1/2: 1/4] = 136.49309008087076
[4/7, 1/2: 1/4] = 136.49309008087076

[3/7, 1/2: 2/7] = 129.75633481662646
[4/7, 1/2: 2/7] = 129.75633481662646

[3/7, 1/2: 1/3] = 120.85441671090702
[4/7, 1/2: 1/3] = 120.85441671090702

[3/7, 1/2: 3/8] = 113.11169443450945
[4/7, 1/2: 3/8] = 113.11169443450945

[3/7, 1/2: 2/5] = 108.47941597800016
[4/7, 1/2: 2/5] = 108.47941597800016

[3/7, 1/2: 3/7] = 103.19367977067233
[4/7, 1/2: 3/7] = 103.19367977067233

[3/7, 1/2: 4/7] = 76.80632022932767
[4/7, 1/2: 4/7] = 76.80632022932767

[3/7, 1/2: 3/5] = 71.52058402199985
[4/7, 1/2: 3/5] = 71.52058402199985

[3/7, 1/2: 5/8] = 66.88830556549055
[4/7, 1/2: 5/8] = 66.88830556549055

[3/7, 1/2: 2/3] = 59.145583289093004
[4/7, 1/2: 2/3] = 59.145583289093004

[3/7, 1/2: 5/7] = 50.24366518337358
[4/7, 1/2: 5/7] = 50.24366518337358

[3/7, 1/2: 3/4] = 43.50690991912927
[4/7, 1/2: 3/4] = 43.50690991912927

[3/7, 1/2: 4/5] = 33.91950417864636
[4/7, 1/2: 4/5] = 33.91950417864636

[3/7, 1/2: 5/6] = 27.339994716998067
[4/7, 1/2: 5/6] = 27.339994716998067

[3/7, 1/2: 6/7] = 22.461126230712722
[4/7, 1/2: 6/7] = 22.461126230712722

[3/7, 1/2: 7/8] = 18.62326536823596
[4/7, 1/2: 7/8] = 18.62326536823596

[3/7, 1/3: 3/7] = 97.57225756692237
[4/7, 1/3: 1/2] = 97.57225756692239

[3/7, 1/3: 1/2] = 82.42774243307763
[4/7, 1/3: 4/7] = 82.42774243307763