The number and percentage of non-overlapping edge unfoldings in Johnson solids.
| Johnson solids | |V| | |E| | |F| | # MOPEs | # edge unfoldings [HS13] | # non-overlapping edge unfoldings | Percentage (%) |
|---|---|---|---|---|---|---|---|
| Elongated pentagonal cupola (J20) | 25 | 45 | 22 | 40 | 29,821,320,745 | 27,158,087,415 | 91.0 |
| Elongated pentagonal rotunda (J21) | 30 | 55 | 27 | 90 | 8,223,103,375,490 | 6,297,186,667,720 | 76.5 |
| Gyroelongated pentagonal cupola (J24) | 25 | 55 | 32 | 60 | 5,996,600,870,820 | 5,492,624,228,190 | 91.5 |
| Pentagonal orthocupolarotunda (J32) | 25 | 50 | 27 | 20 | 699,537,024,120 | 699,433,603,320 | 99.9 |
| Pentagonal gyrocupolarotunda (J33) | 25 | 50 | 27 | 10 | 745,208,449,920 | 745,198,979,400 | 99.9 |
| Pentagonal orthobirotunda (J34) | 30 | 60 | 32 | 10 | 193,003,269,869,040 | 190,653,702,525,040 | 98.7 |
| Elongated pentagonal orthobicupola (J38) | 30 | 60 | 32 | 80 | 270,745,016,304,350 | 214,085,775,357,270 | 79.0 |
| Elongated pentagonal gyrobicupola (J39) | 30 | 60 | 32 | 80 | 272,026,496,000,000 | 215,087,798,524,180 | 79.0 |
| Gyroelongated triangular bicupola (J44) | 18 | 42 | 26 | 24 | 5,295,528,588 | 5,231,781,954 | 98.7 |
| Gyroelongated square bicupola (J45) | 24 | 56 | 34 | 48 | 13,769,880,349,680 | 13,386,219,088,644 | 97.2 |
| Augmented hexagonal prism (J54) | 13 | 22 | 11 | 4 | 75,973 | 75,749 | 99.7 |
| Parabiaugmented hexagonal prism (J55) | 14 | 26 | 14 | 8 | 709,632 | 705,144 | 99.4 |
| Metabiaugmented hexagonal prism (J56) | 14 | 26 | 14 | 8 | 707,232 | 702,520 | 99.3 |
| Triaugmented hexagonal prism (J57) | 15 | 30 | 17 | 12 | 6,531,840 | 6,457,860 | 98.9 |
| Augmented dodecahedron (J58) | 21 | 35 | 16 | 5 | 92,724,962 | 92,219,782 | 99.4 |
| Parabiaugmented dodecahedron (J59) | 22 | 40 | 20 | 10 | 1,651,482,010 | 1,632,941,030 | 98.8 |
| Metabiaugmented dodecahedron (J60) | 22 | 40 | 20 | 10 | 1,641,317,568 | 1,621,738,522 | 98.8 |
| Triaugmented dodecahedron (J61) | 23 | 45 | 24 | 15 | 28,745,798,400 | 28,183,512,978 | 98.0 |
| Augmented truncated cube (J66) | 28 | 48 | 22 | 104 | 54,921,311,280 | 39,055,563,000 | 71.1 |
| Biaugmented truncated cube (J67) | 32 | 60 | 30 | 208 | 90,974,647,120,896 | 43,437,626,181,464 | 47.7 |
The number and percentage of non-overlapping edge unfoldings in Archimedian prisms.
| Archimedian n-prism | |V| | |E| | |F| | # MOPEs | # edge unfoldings [HS13] | # non-overlapping edge unfoldings | Percentage (%) |
|---|---|---|---|---|---|---|---|
| Archimedian 24-prism | 48 | 72 | 26 | 96 | 639,620,518,118,400 | 597,547,526,278,102 | 93.4 |
| Archimedian 25-prism | 50 | 75 | 27 | 100 | 2,486,558,615,814,025 | 2,270,951,013,426,531 | 91.3 |
| Archimedian 26-prism | 52 | 78 | 28 | 208 | 9,651,161,613,824,796 | 8,680,724,875,408,147 | 89.9 |
| Archimedian 27-prism | 54 | 81 | 29 | 216 | 37,403,957,244,654,675 | 33,593,039,475,394,304 | 89.8 |
| Archimedian 28-prism | 56 | 84 | 30 | 336 | 144,763,597,316,784,768 | 128,484,071,528,042,868 | 88.7 |
| Archimedian 29-prism | 58 | 87 | 31 | 580 | 559,560,282,425,278,229 | 273,052,412,937,434,749 | 48.7 |
| Archimedian 30-prism | 60 | 90 | 32 | 720 | 2,160,318,004,043,512,500 | 1,012,562,467,010,055,179 | 46.8 |
| Archimedian 31-prism | 62 | 93 | 33 | 744 | 8,331,163,769,982,715,231 | 3,755,308,489,795,021,132 | 45.0 |
| Archimedian 32-prism | 64 | 96 | 34 | 768 | 32,095,304,749,163,937,792 | 13,910,558,120,316,453,216 | 43.3 |
| Archimedian 33-prism | 66 | 99 | 35 | 792 | 123,524,473,883,545,449,825 | 51,464,102,399,119,841,064 | 41.6 |
| Archimedian 34-prism | 68 | 102 | 36 | 952 | 474,969,297,739,230,927,564 | 190,077,650,531,107,175,354 | 40.0 |
| Archimedian 35-prism | 70 | 105 | 37 | 1,120 | 1,824,745,126,233,358,110,635 | 694,876,093,525,600,562,317 | 38.0 |
| Archimedian 36-prism | 72 | 108 | 38 | 1,440 | 7,004,614,136,879,907,849,600 | 2,380,408,316,368,094,877,275 | 33.9 |
| Archimedian 37-prism | 74 | 111 | 39 | 1,776 | 26,867,730,730,869,118,775,917 | 8,734,608,096,670,703,034,258 | 32.5 |
| Archimedian 38-prism | 76 | 114 | 40 | 2,128 | 102,981,783,095,242,242,871,908 | 31,927,951,665,245,016,746,682 | 31.0 |
| Archimedian 39-prism | 78 | 117 | 41 | 2,496 | 394,447,279,575,099,709,694,775 | 117,143,971,138,672,055,381,811 | 29.6 |
| Archimedian 40-prism | 80 | 120 | 42 | 2,880 | 1,509,843,372,596,510,348,221,440 | 385,268,000,158,423,393,347,888 | 25.5 |
| Archimedian 41-prism | 82 | 123 | 43 | 3,116 | 5,775,682,482,451,356,835,464,761 | 1,409,268,044,697,380,611,870,787 | 24.4 |
| Archimedian 42-prism | 84 | 126 | 44 | 3,360 | 22,080,875,606,379,223,850,418,300 | 5,178,957,938,434,484,085,594,343 | 23.4 |
The number and percentage of non-overlapping edge unfoldings in Archimedian antiprisms.
| Archimedian m-antiprism | |V| | |E| | |F| | # MOPEs | # edge unfoldings [HS13] | # non-overlapping edge unfoldings | Percentage (%) |
|---|---|---|---|---|---|---|---|
| Archimedian 12-antiprism | 24 | 48 | 26 | 48 | 51,599,794,176 | 49,743,531,024 | 96.4 |
| Archimedian 13-antiprism | 26 | 52 | 28 | 52 | 383,142,771,674 | 369,359,503,344 | 96.4 |
| Archimedian 14-antiprism | 28 | 56 | 30 | 56 | 2,828,107,288,188 | 2,726,368,290,352 | 96.4 |
| Archimedian 15-antiprism | 30 | 60 | 32 | 60 | 20,768,716,848,000 | 20,021,578,135,380 | 96.4 |
| Archimedian 16-antiprism | 32 | 64 | 34 | 64 | 151,840,963,183,392 | 146,378,600,602,880 | 96.4 |
| Archimedian 17-antiprism | 34 | 68 | 36 | 136 | 1,105,779,284,582,146 | 1,013,491,325,102,942 | 91.6 |
| Archimedian 18-antiprism | 36 | 72 | 38 | 360 | 8,024,954,790,380,544 | 1,501,154,452,845,906 | 18.7 |
| Archimedian 19-antiprism | 38 | 76 | 40 | 380 | 58,059,628,319,357,318 | 13,038,527,513,687,486 | 22.4 |
| Archimedian 20-antiprism | 40 | 80 | 42 | 480 | 418,891,171,182,561,000 | 98,027,112,294,661,196 | 23.4 |
| Archimedian 21-antiprism | 42 | 84 | 44 | 588 | 3,014,678,940,049,375,872 | 732,157,627,679,302,758 | 24.2 |
| Archimedian 22-antiprism | 44 | 88 | 46 | 616 | 21,646,865,272,061,272,716 | 5,463,662,878,677,088,327 | 25.2 |
| Archimedian 23-antiprism | 46 | 92 | 48 | 644 | 155,113,904,634,576,144,814 | 40,508,628,620,513,122,070 | 26.1 |
| Archimedian 24-antiprism | 48 | 96 | 50 | 864 | 1,109,391,149,998,449,819,648 | 298,293,520,418,401,464,964 | 26.8 |
| Archimedian 25-antiprism | 50 | 100 | 52 | 900 | 7,920,708,398,483,722,531,250 | 2,188,171,009,006,050,804,805 | 27.6 |
| Archimedian 26-antiprism | 52 | 104 | 54 | 936 | 56,460,916,728,463,179,389,652 | 15,982,421,259,908,162,238,792 | 28.3 |
| Archimedian 27-antiprism | 54 | 108 | 56 | 1,296 | 401,873,068,071,158,383,691,136 | 100,599,073,148,261,099,923,798 | 25.0 |
| Archimedian 28-antiprism | 56 | 112 | 58 | 1,568 | 2,856,496,726,273,368,888,420,984 | 725,756,982,845,834,563,864,391 | 25.4 |
| Archimedian 29-antiprism | 58 | 116 | 60 | 1,856 | 20,277,959,821,998,087,658,569,178 | 5,224,196,129,087,410,893,943,357 | 25.7 |
| Archimedian 30-antiprism | 60 | 120 | 62 | 2,160 | 143,779,866,504,299,168,102,784,000 | 37,518,568,275,655,316,428,289,607 | 26.0 |
| Archimedian 31-antiprism | 62 | 124 | 64 | 2,480 | 1,018,331,261,238,041,888,906,149,982 | 272,565,329,790,964,088,373,433,340 | 26.7 |
| Archimedian 32-antiprism | 64 | 128 | 66 | 2,560 | 7,204,899,406,395,028,729,775,662,656 | 2,207,488,168,172,480,018,238,295,855 | 30.6 |
[HS13] Takashi Horiyama and Wataru Shoji. The number of different unfoldings of polyhedra. In 24th International Symposium on Algorithms and Computation, volume 8283 of LNCS, pages 623–633. Springer, 2013.