This table was calculated by Mike Masonjones. It took approximately one year on a dedicated but slow pc (800Mhz). The bulk of the time was spent doing disk access. A further week or so was needed to read through the full database to distill the table below.
The calculations were done in the twist metric, i.e. only twists of half the puzzle were counted. This allowed positions that differ by layer turns to be treated as identical, and so kept the size of the database files down. Even so, the final result is still several Gigabytes in total.
The first column of the table shows the shapes. I have lumped together similar shapes (same by reflection or rotation) since they will obviously have the same numbers. The table shows that every position can be solved in at most 13 twists, or 12 if the middle layer is ignored.
| Shapes | All Depths | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| cececece/cececece | 203212800 | 1 | 32 | 433 | 4842 | 50424 | 496354 | 4356750 | 25756434 | 46028208 | 25614194 | 19053576 | 49529984 | 32117008 | 204560 |
| ceeeeceeee/cccccc cccccc/ceeeeceeee | 270950400 | 0 | 0 | 0 | 0 | 64 | 1856 | 33728 | 515392 | 6555968 | 52421920 | 124122336 | 82536032 | 4763104 | 0 |
| cceeccee/cececece cececece/cceeccee | 406425600 | 0 | 0 | 0 | 0 | 0 | 0 | 448 | 33504 | 949552 | 18120096 | 143842176 | 185056816 | 58420624 | 2384 |
| cceeeeeeee/cccccc cccccc/cceeeeeeee | 541900800 | 0 | 0 | 0 | 0 | 64 | 2048 | 43008 | 735936 | 10145984 | 88956960 | 244998048 | 181255424 | 15763296 | 32 |
| ceeceeeeee/cccccc cccccc/ceeceeeeee | 541900800 | 0 | 0 | 0 | 0 | 64 | 1664 | 34560 | 647552 | 9684672 | 89058912 | 247442336 | 181242272 | 13788768 | 0 |
| ceceeeeeee/cccccc cccccc/ceceeeeeee | 541900800 | 0 | 0 | 0 | 0 | 0 | 0 | 960 | 43040 | 1152320 | 21737184 | 181502048 | 249156800 | 88295072 | 13376 |
| ceeeeeceee/cccccc cccccc/ceeeeeceee | 541900800 | 0 | 0 | 0 | 0 | 0 | 0 | 608 | 43424 | 1248896 | 23491392 | 188124736 | 247407552 | 81576160 | 8032 |
| cceeccee/cceeccee | 812851200 | 0 | 0 | 16 | 400 | 6128 | 77600 | 892224 | 9323408 | 72924832 | 235458048 | 309914592 | 161565952 | 22687808 | 192 |
| ccceecee/cececece cececece/ccceecee | 812851200 | 0 | 0 | 0 | 128 | 2848 | 44672 | 594768 | 6764104 | 56411824 | 192441176 | 270343184 | 207082312 | 79072976 | 93208 |
| cceeecce/cececece cececece/cceeecce | 812851200 | 0 | 0 | 0 | 128 | 2848 | 44672 | 590864 | 6676616 | 55370000 | 184885264 | 239377672 | 214229168 | 111084216 | 589752 |
| ccceceee/cececece cececece/ccceeece ccceeece/cececece cececece/ccceceee | 812851200 | 0 | 0 | 0 | 0 | 0 | 640 | 20128 | 397840 | 6212744 | 72149288 | 329850768 | 333869016 | 70341960 | 8816 |
| cccceeee/cececece cececece/cccceeee | 812851200 | 0 | 0 | 0 | 0 | 0 | 384 | 14336 | 329696 | 5705808 | 71343056 | 338214144 | 334751760 | 62491312 | 704 |
| cececece/cececeec cececeec/cececece cceecece/cececece cececece/cceecece | 812851200 | 0 | 0 | 0 | 0 | 0 | 0 | 832 | 42752 | 1263104 | 26485216 | 254017248 | 379776336 | 151144416 | 121296 |
| cececece/ceceecec ceceecec/cececece | 812851200 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10240 | 490048 | 13576720 | 188391696 | 392390576 | 217543856 | 448064 |
| ceeceecee/cccccee cccccee/ceeceecee | 1083801600 | 0 | 0 | 0 | 0 | 256 | 7808 | 148992 | 2308800 | 28885888 | 220537216 | 495417984 | 319046976 | 17447680 | 0 |
| ceeceecee/ccccece ccccece/ceeceecee | 1083801600 | 0 | 0 | 0 | 0 | 0 | 0 | 4096 | 133504 | 2831936 | 45162816 | 352244736 | 496498688 | 186820032 | 105792 |
| ceeceecee/cccecce cccecce/ceeceecee | 1083801600 | 0 | 0 | 0 | 0 | 0 | 0 | 1984 | 64960 | 1373056 | 22558976 | 227917632 | 515214592 | 312608128 | 4062272 |
| cceeccee/ceceecec ceceecec/cceeccee | 1625702400 | 0 | 0 | 0 | 64 | 1792 | 35648 | 558144 | 7103424 | 68560864 | 317064416 | 498386080 | 486692960 | 245344320 | 1954688 |
| cccceeee/cceeccee cceeccee/cccceeee | 1625702400 | 0 | 0 | 0 | 0 | 256 | 8832 | 184000 | 3023264 | 38823360 | 298084128 | 723124608 | 511734720 | 50718976 | 256 |
| ccceecee/cceeccee cceeccee/ccceecee | 1625702400 | 0 | 0 | 0 | 0 | 0 | 1152 | 50944 | 1278016 | 21466752 | 211137504 | 700294208 | 600433696 | 91039296 | 832 |
| ccceceee/cceeccee cceeccee/ccceeece ccceeece/cceeccee cceeccee/ccceceee | 1625702400 | 0 | 0 | 0 | 0 | 0 | 128 | 7232 | 211584 | 4516976 | 73085408 | 550768736 | 739417248 | 257558256 | 136832 |
| cceeccee/cceeecce cceeecce/cceeccee | 1625702400 | 0 | 0 | 0 | 0 | 0 | 0 | 2688 | 102016 | 2412256 | 43421536 | 427908128 | 768607008 | 382528128 | 720640 |
| cceeccee/cceecece cceecece/cceeccee cececeec/cceeccee cceeccee/cececeec | 1625702400 | 0 | 0 | 0 | 0 | 0 | 0 | 960 | 80064 | 2767104 | 60680448 | 558566000 | 752050384 | 251517136 | 40304 |
| ceceecec/ceceecec | 3251404800 | 0 | 32 | 576 | 7520 | 87200 | 937024 | 9483936 | 84080704 | 466269504 | 752979648 | 633919808 | 775750528 | 515941376 | 11946944 |
| cceecece/cececeec cececeec/cceecece | 3251404800 | 0 | 0 | 64 | 1536 | 24960 | 339200 | 4072800 | 42624288 | 308894304 | 774391520 | 877145504 | 806124000 | 435564768 | 2221856 |
| ccceecee/ccceecee | 3251404800 | 0 | 0 | 0 | 128 | 3584 | 63232 | 926592 | 11977504 | 127866528 | 779917536 | 1436852896 | 833743936 | 60052800 | 64 |
| cceeecce/cceeecce | 3251404800 | 0 | 0 | 0 | 128 | 3456 | 56576 | 755584 | 8992128 | 91836160 | 577502464 | 1283492352 | 1039074560 | 249614848 | 76544 |
| cccceeee/cccceeee | 3251404800 | 0 | 0 | 0 | 64 | 1856 | 33792 | 513472 | 7128960 | 85727168 | 654021696 | 1485339008 | 964517760 | 54120896 | 128 |
| ccceceee/ccceeece ccceeece/ccceceee | 3251404800 | 0 | 0 | 0 | 64 | 1600 | 26880 | 379456 | 4791904 | 53640224 | 429300736 | 1322820160 | 1191491136 | 248860960 | 91680 |
| cccceeee/ceceecec ceceecec/cccceeee | 3251404800 | 0 | 0 | 0 | 64 | 1536 | 25728 | 368448 | 4723872 | 53039296 | 408022912 | 1207836608 | 1212225696 | 364456512 | 704128 |
| ccceceee/cececeec cececeec/ccceceee ccceeece/cceecece cceecece/ccceeece | 3251404800 | 0 | 0 | 0 | 0 | 1152 | 28960 | 488064 | 6714400 | 74089312 | 491329056 | 1159739872 | 1126267360 | 391384000 | 1362624 |
| ceceeceee/ccccece ccccece/ceceeceee ceceeecee/ccccece ccccece/ceceeecee | 3251404800 | 0 | 0 | 0 | 0 | 512 | 13824 | 246688 | 3626528 | 45010688 | 395918592 | 1321531072 | 1226080672 | 258913440 | 62784 |
| ccceecee/cceeecce cceeecce/ccceecee | 3251404800 | 0 | 0 | 0 | 0 | 352 | 10784 | 219072 | 3485536 | 44114944 | 363009120 | 1101764608 | 1255821664 | 479603424 | 3375296 |
| cceeceeee/cccccee cccccee/cceeceeee cceeeecee/cccccee cccccee/cceeeecee | 3251404800 | 0 | 0 | 0 | 0 | 192 | 8448 | 215168 | 4114496 | 59773216 | 525977344 | 1461192192 | 1095602048 | 104521632 | 64 |
| ccceeeeee/cccccee cccccee/ccceeeeee | 3251404800 | 0 | 0 | 0 | 0 | 128 | 6656 | 181632 | 3600576 | 53828992 | 491939328 | 1451892352 | 1130155776 | 119799296 | 64 |
| cececeeee/cccccee cccccee/cececeeee | 3251404800 | 0 | 0 | 0 | 0 | 128 | 5760 | 129472 | 2219072 | 32027392 | 348255232 | 1414301696 | 1275221952 | 179243712 | 384 |
| cececeeee/ccccece ccccece/cececeeee | 3251404800 | 0 | 0 | 0 | 0 | 128 | 4608 | 106112 | 1907840 | 28616064 | 322969920 | 1389881792 | 1300818944 | 207098304 | 1088 |
| cceeeceee/ccccece ccccece/cceeeceee | 3251404800 | 0 | 0 | 0 | 0 | 128 | 3328 | 68864 | 1175232 | 17354752 | 209394368 | 1209565760 | 1415087808 | 398712896 | 41664 |
| cceeeeece/ccccece ccccece/cceeeeece ceceeeeec/ccccece ccccece/ceceeeeec | 3251404800 | 0 | 0 | 0 | 0 | 64 | 2944 | 68928 | 1250016 | 18988928 | 224473344 | 1203811232 | 1399802624 | 402833248 | 173472 |
| cceeceeee/cccecce cccecce/cceeceeee cceeeecee/cccecce cccecce/cceeeecee | 3251404800 | 0 | 0 | 0 | 0 | 64 | 2016 | 41024 | 709376 | 10812960 | 136104576 | 928514272 | 1483515584 | 686334080 | 5370848 |
| cceeeeece/cccccee cccccee/cceeeeece ceceeeeec/cccccee cccccee/ceceeeeec | 3251404800 | 0 | 0 | 0 | 0 | 64 | 1664 | 38016 | 766080 | 13279776 | 185485024 | 1185556960 | 1439389632 | 426827584 | 60000 |
| cccceeee/ccceecee ccceecee/cccceeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 2560 | 108864 | 2683712 | 44538368 | 434644224 | 1417536256 | 1188371712 | 163518912 | 192 |
| ceceeceee/cccccee cccccee/ceceeceee ceceeecee/cccccee cccccee/ceceeecee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 1920 | 56992 | 1140416 | 18574560 | 232922240 | 1259614272 | 1391600832 | 347456576 | 36992 |
| cceeceeee/ccccece ccccece/cceeceeee cceeeecee/ccccece ccccece/cceeeecee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 1536 | 50336 | 1046336 | 17396800 | 222208032 | 1236014464 | 1402378272 | 372240800 | 68224 |
| ceceeceee/cccecce cccecce/ceceeceee ceceeecee/cccecce cccecce/ceceeecee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 1472 | 41600 | 808512 | 12832576 | 158333312 | 989377312 | 1462481952 | 623450912 | 4077152 |
| ceceecec/ccceecee ccceecee/ceceecec | 3251404800 | 0 | 0 | 0 | 0 | 0 | 1024 | 31168 | 629568 | 10441728 | 141278272 | 1015149760 | 1483176768 | 600079744 | 616768 |
| cceeeceee/cccccee cccccee/cceeeceee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 960 | 35776 | 825536 | 14833920 | 204015872 | 1232710208 | 1420843584 | 378122496 | 16448 |
| ccceeece/ccceeece ccceceee/ccceceee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 896 | 32608 | 672064 | 11245568 | 151416800 | 1048248352 | 1473010080 | 566175872 | 602560 |
| ccceceee/ceceecec ceceecec/ccceceee ccceeece/ceceecec ceceecec/ccceeece | 3251404800 | 0 | 0 | 0 | 0 | 0 | 832 | 28448 | 617536 | 10756800 | 146770784 | 1015659936 | 1477030656 | 599257216 | 1282592 |
| cceeeeece/cccecce cccecce/ceceeeeec ceceeeeec/cccecce cccecce/cceeeeece | 3251404800 | 0 | 0 | 0 | 0 | 0 | 768 | 29792 | 689056 | 12301536 | 164059072 | 1040801344 | 1459679264 | 572569728 | 1274240 |
| ccceceee/cceecece cceecece/ccceceee ccceeece/cececeec cececeec/ccceeece | 3251404800 | 0 | 0 | 0 | 0 | 0 | 768 | 28096 | 628480 | 11063232 | 153656672 | 1066654464 | 1471064800 | 547956608 | 351680 |
| cccceeee/cceecece cceecece/cccceeee cccceeee/cececeec cececeec/cccceeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 512 | 27200 | 712544 | 13686080 | 197865120 | 1224497248 | 1427069696 | 387491872 | 54528 |
| ccceeeeee/cccecce cccecce/ccceeeeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 512 | 16384 | 355520 | 6416704 | 94343808 | 811189184 | 1523908416 | 808080128 | 7094144 |
| cceeeceee/cccecce cccecce/cceeeceee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 384 | 19968 | 566912 | 11604928 | 167762688 | 1065406144 | 1456606080 | 548671360 | 766336 |
| ccceceee/cceeecce cceeecce/ccceceee ccceeece/cceeecce cceeecce/ccceeece | 3251404800 | 0 | 0 | 0 | 0 | 0 | 384 | 18560 | 508576 | 10283520 | 153066560 | 1064207840 | 1471739200 | 551192480 | 387680 |
| ccceeeeee/ccccece ccccece/ccceeeeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 384 | 16768 | 436800 | 8685248 | 136291328 | 1058548864 | 1488706304 | 558451520 | 267584 |
| cccceeee/cceeecce cceeecce/cccceeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 384 | 12096 | 284352 | 5674816 | 93529856 | 875636352 | 1530381312 | 744379136 | 1506496 |
| cccceeee/ccceceee ccceceee/cccceeee cccceeee/ccceeece ccceeece/cccceeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 256 | 12448 | 339392 | 7122368 | 118361728 | 1003414144 | 1506607968 | 615153440 | 393056 |
| ccceecee/cceecece cceecece/ccceecee ccceecee/cececeec cececeec/ccceecee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 128 | 11968 | 390880 | 8669120 | 144557344 | 1110685600 | 1480492576 | 506335712 | 261472 |
| cececeeee/cccecce cccecce/cececeeee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 128 | 11392 | 333824 | 6702720 | 103537856 | 881996160 | 1519426624 | 736992128 | 2403968 |
| ccceceee/ccceecee ccceecee/ccceceee ccceecee/ccceeece ccceeece/ccceecee | 3251404800 | 0 | 0 | 0 | 0 | 0 | 64 | 10624 | 348384 | 7674112 | 127665632 | 1041163424 | 1497404288 | 576854240 | 284032 |
| cceeecce/ceceecec ceceecec/cceeecce | 3251404800 | 0 | 0 | 0 | 0 | 0 | 0 | 6144 | 276032 | 6992192 | 117638656 | 926066048 | 1505936448 | 692638016 | 1851264 |
| cceecece/cceecece cececeec/cececeec | 3251404800 | 0 | 0 | 0 | 0 | 0 | 0 | 5120 | 215232 | 5712224 | 108580512 | 985470272 | 1516513184 | 634514784 | 393472 |
| cceecece/ceceecec ceceecec/cceecece cececeec/ceceecec ceceecec/cececeec | 3251404800 | 0 | 0 | 0 | 0 | 0 | 0 | 2688 | 115744 | 3169600 | 66108960 | 777815520 | 1555725344 | 844714592 | 3752352 |
| cceecece/cceeecce cceeecce/cceecece cececeec/cceeecce cceeecce/cececeec | 3251404800 | 0 | 0 | 0 | 0 | 0 | 0 | 2240 | 123328 | 3666880 | 76967904 | 857571840 | 1546843840 | 764461440 | 1767328 |
| Totals | 435891456000 | 1 | 64 | 1153 | 17050 | 235144 | 3091458 | 38893230 | 452031138 | 4459167504 | 33671064770 | 149502310936 | 183662070768 | 63945120032 | 157452752 |