Bounds and Dimensions on generic Powell-Sabin
r |
d |
pol | |
l.b. |
dim |
c.u.b. |
s.u.b. |
|
M |
N |
rank |
MDS |
delta |
mods |
1 |
1 |
4 | |
4 |
4 |
4 |
4 |
|
39 |
14 |
10 |
4 |
100 |
7,363 |
1 |
2 |
10 | |
10 |
11 |
11 |
20 |
|
117 |
60 |
49 |
11 |
69 |
183,651 |
1 |
3 |
20 | |
34 |
36 |
37 |
60 |
|
234 |
163 |
127 |
36 |
67 |
1,186,737 |
1 |
4 |
35 | |
100 |
102 |
106 |
145 |
|
390 |
347 |
245 |
102 |
50 |
5,452,265 |
1 |
5 |
56 | |
232 |
234 |
242 |
296 |
|
585 |
636 |
402 |
234 |
37 |
18,879,498 |
1 |
6 |
84 | |
454 |
456 |
469 |
537 |
|
819 |
1036 |
598 |
438 |
33 |
51,242,353 |
1 |
7 |
120 | |
790 |
792 |
811 |
892 |
|
1092 |
1553 |
833 |
720 |
30 |
118,685,250 |
1 |
8 |
165 | |
1264 |
1266 |
1292 |
1385 |
|
1404 |
2187 |
1107 |
1080 |
28 |
242,330,911 |
1 |
9 |
220 | |
1900 |
1902 |
1936 |
2040 |
|
1755 |
2938 |
1420 |
1518 |
27 |
457,943,345 |
1 |
10 |
286 | |
2722 |
2724 |
2767 |
2881 |
|
2145 |
3806 |
1772 |
2034 |
26 |
785,138,492 |
1 |
11 |
364 | |
3754 |
3756 |
3809 |
3932 |
|
2574 |
4791 |
2163 |
2628 |
26 |
1,283,007,421 |
1 |
12 |
455 | |
5020 |
5022 |
5086 |
5217 |
|
3042 |
5893 |
2593 |
3300 |
25 |
2,022,793,536 |
1 |
13 |
560 | |
6544 |
6546 |
6622 |
6760 |
|
3549 |
7112 |
3062 |
4050 |
25 |
3,013,026,367 |
1 |
14 |
680 | |
8350 |
8352 |
8441 |
8585 |
|
4095 |
8448 |
3570 |
4878 |
24 |
4,391,309,355 |
1 |
15 |
816 | |
10462 |
10464 |
10567 |
10716 |
|
4680 |
9901 |
4117 |
5784 |
24 |
6,405,770,350 |
1 |
16 |
969 | |
12904 |
12906 |
13024 |
13177 |
|
5304 |
11471 |
4703 |
6768 |
24 |
8,938,201,802 |
1 |
17 |
1140 | |
15700 |
15702 |
15836 |
15992 |
|
5967 |
13158 |
5328 |
7830 |
24 |
11,869,733,651 |
1 |
18 |
1330 | |
18874 |
18876 |
19027 |
19185 |
|
6669 |
14962 |
5992 |
8970 |
23 |
15,884,599,275 |
1 |
19 |
1540 | |
22450 |
22452 |
22621 |
22780 |
|
7410 |
16883 |
6695 |
10188 |
23 |
21,215,735,340 |
1 |
20 |
1771 | |
26452 |
26454 |
26642 |
26801 |
|
8190 |
18921 |
7437 |
11484 |
23 |
27,576,297,866 |
1 |
21 |
2024 | |
30904 |
30906 |
31114 |
31272 |
|
9009 |
21076 |
8218 |
12858 |
23 |
34,667,383,398 |
1 |
22 |
2300 | |
35830 |
35832 |
36061 |
36217 |
|
9867 |
23348 |
9038 |
14310 |
23 |
43,952,800,982 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
156 |
60 |
50 |
10 |
78 |
233,863 |
2 |
3 |
20 | |
10 |
21 |
21 |
30 |
|
351 |
163 |
142 |
21 |
71 |
2,252,759 |
2 |
4 |
35 | |
16 |
41 |
42 |
75 |
|
624 |
347 |
306 |
41 |
77 |
12,254,719 |
2 |
5 |
56 | |
49 |
87 |
92 |
156 |
|
975 |
636 |
549 |
87 |
74 |
48,605,350 |
2 |
6 |
84 | |
133 |
183 |
195 |
294 |
|
1404 |
1054 |
871 |
183 |
60 |
161,174,347 |
2 |
7 |
120 | |
292 |
354 |
375 |
510 |
|
1911 |
1625 |
1271 |
354 |
46 |
441,287,560 |
2 |
8 |
165 | |
550 |
624 |
656 |
825 |
|
2496 |
2373 |
1749 |
624 |
40 |
1,079,622,288 |
2 |
9 |
220 | |
931 |
1017 |
1062 |
1263 |
|
3159 |
3304 |
2305 |
999 |
39 |
2,236,704,302 |
2 |
10 |
286 | |
1459 |
1557 |
1617 |
1848 |
|
3900 |
4424 |
2939 |
1485 |
35 |
4,349,425,449 |
2 |
11 |
364 | |
2158 |
2268 |
2345 |
2604 |
|
4719 |
5739 |
3651 |
2088 |
31 |
8,071,731,486 |
2 |
12 |
455 | |
3052 |
3174 |
3270 |
3555 |
|
5616 |
7249 |
4441 |
2808 |
29 |
13,590,068,757 |
2 |
13 |
560 | |
4165 |
4299 |
4416 |
4725 |
|
6591 |
8954 |
5309 |
3645 |
27 |
22,144,062,154 |
2 |
14 |
680 | |
5521 |
5667 |
5807 |
6138 |
|
7644 |
10854 |
6255 |
4599 |
26 |
35,331,290,468 |
2 |
15 |
816 | |
7144 |
7302 |
7467 |
7818 |
|
8775 |
12949 |
7279 |
5670 |
25 |
53,064,928,715 |
2 |
16 |
969 | |
9058 |
9228 |
9420 |
9789 |
|
9984 |
15239 |
8381 |
6858 |
24 |
78,865,459,918 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
390 |
163 |
143 |
20 |
74 |
2,846,109 |
3 |
4 |
35 | |
15 |
36 |
36 |
45 |
|
741 |
347 |
311 |
36 |
79 |
17,563,609 |
3 |
5 |
56 | |
7 |
60 |
60 |
96 |
|
1209 |
636 |
576 |
60 |
81 |
81,962,409 |
3 |
6 |
84 | |
11 |
94 |
103 |
184 |
|
1794 |
1054 |
960 |
94 |
82 |
320,297,543 |
3 |
7 |
120 | |
51 |
162 |
185 |
320 |
|
2496 |
1625 |
1463 |
162 |
80 |
967,124,665 |
3 |
8 |
165 | |
151 |
286 |
330 |
525 |
|
3315 |
2373 |
2087 |
286 |
75 |
2,508,686,875 |
3 |
9 |
220 | |
335 |
493 |
562 |
820 |
|
4251 |
3322 |
2829 |
493 |
68 |
5,381,258,765 |
3 |
10 |
286 | |
627 |
809 |
905 |
1226 |
|
5304 |
4496 |
3687 |
809 |
63 |
11,190,430,796 |
3 |
11 |
364 | |
1051 |
1257 |
1383 |
1764 |
|
6474 |
5919 |
4662 |
1257 |
59 |
20,943,968,245 |
3 |
12 |
455 | |
1631 |
1861 |
2020 |
2458 |
|
7761 |
7597 |
5754 |
1843 |
56 |
37,789,942,844 |
3 |
13 |
560 | |
2391 |
2645 |
2840 |
3332 |
|
9165 |
9536 |
6963 |
2573 |
54 |
61,843,150,846 |
3 |
14 |
680 | |
3355 |
3633 |
3867 |
4410 |
|
10686 |
11742 |
8289 |
3453 |
52 |
100,906,443,654 |
3 |
15 |
816 | |
4547 |
4849 |
5125 |
5716 |
|
12324 |
14221 |
9732 |
4489 |
50 |
155,912,689,734 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
780 |
347 |
312 |
35 |
81 |
20,648,995 |
4 |
5 |
56 | |
26 |
57 |
57 |
66 |
|
1326 |
636 |
579 |
57 |
83 |
105,771,900 |
4 |
6 |
84 | |
5 |
88 |
88 |
124 |
|
2028 |
1054 |
966 |
88 |
86 |
437,044,792 |
4 |
7 |
120 | |
-16 |
130 |
131 |
220 |
|
2886 |
1625 |
1495 |
130 |
86 |
1,492,516,789 |
4 |
8 |
165 | |
-16 |
190 |
203 |
365 |
|
3900 |
2373 |
2183 |
190 |
86 |
4,204,748,647 |
4 |
9 |
220 | |
29 |
294 |
324 |
570 |
|
5070 |
3322 |
3028 |
294 |
87 |
10,264,741,492 |
4 |
10 |
286 | |
143 |
463 |
518 |
856 |
|
6396 |
4496 |
4033 |
463 |
82 |
22,494,486,419 |
4 |
11 |
364 | |
350 |
719 |
809 |
1244 |
|
7878 |
5919 |
5200 |
719 |
76 |
43,838,197,970 |
4 |
12 |
455 | |
674 |
1093 |
1221 |
1755 |
|
9516 |
7615 |
6522 |
1093 |
71 |
82,936,920,308 |
4 |
13 |
560 | |
1139 |
1609 |
1778 |
2410 |
|
11310 |
9608 |
7999 |
1609 |
65 |
146,188,951,345 |
4 |
14 |
680 | |
1769 |
2290 |
2504 |
3230 |
|
13260 |
11922 |
9632 |
2290 |
60 |
239,538,730,486 |
4 |
15 |
816 | |
2588 |
3160 |
3423 |
4239 |
|
15366 |
14563 |
11421 |
3142 |
58 |
380,864,004,967 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1365 |
636 |
580 |
56 |
85 |
115,364,219 |
5 |
6 |
84 | |
44 |
85 |
85 |
94 |
|
2145 |
1054 |
969 |
85 |
88 |
507,136,196 |
5 |
7 |
120 | |
11 |
124 |
124 |
160 |
|
3120 |
1625 |
1501 |
124 |
89 |
1,873,832,126 |
5 |
8 |
165 | |
-31 |
175 |
175 |
265 |
|
4290 |
2373 |
2198 |
175 |
85 |
5,600,813,984 |
5 |
9 |
220 | |
-67 |
240 |
245 |
420 |
|
5655 |
3322 |
3082 |
240 |
86 |
14,770,699,363 |
5 |
10 |
286 | |
-73 |
328 |
354 |
636 |
|
7215 |
4496 |
4168 |
328 |
86 |
33,812,469,017 |
5 |
11 |
364 | |
-25 |
470 |
522 |
924 |
|
8970 |
5919 |
5449 |
470 |
86 |
69,930,119,093 |
5 |
12 |
455 | |
101 |
686 |
773 |
1305 |
|
10920 |
7615 |
6929 |
686 |
85 |
133,211,207,539 |
5 |
13 |
560 | |
329 |
997 |
1131 |
1800 |
|
13065 |
9608 |
8611 |
997 |
81 |
239,116,752,344 |
5 |
14 |
680 | |
683 |
1431 |
1620 |
2430 |
|
15405 |
11922 |
10491 |
1431 |
77 |
406,968,000,798 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2184 |
1054 |
970 |
84 |
89 |
546,598,446 |
6 |
7 |
120 | |
70 |
121 |
121 |
130 |
|
3237 |
1625 |
1504 |
121 |
91 |
2,071,317,450 |
6 |
8 |
165 | |
26 |
169 |
169 |
205 |
|
4524 |
2373 |
2204 |
169 |
88 |
6,522,874,514 |
6 |
9 |
220 | |
-36 |
230 |
230 |
320 |
|
6045 |
3322 |
3092 |
230 |
87 |
17,646,593,702 |
6 |
10 |
286 | |
-104 |
306 |
306 |
486 |
|
7800 |
4496 |
4190 |
306 |
86 |
41,071,539,008 |
6 |
11 |
364 | |
-157 |
400 |
411 |
714 |
|
9789 |
5919 |
5519 |
400 |
86 |
89,407,903,538 |
6 |
12 |
455 | |
-171 |
525 |
565 |
1015 |
|
12012 |
7615 |
7090 |
525 |
88 |
175,940,372,060 |
6 |
13 |
560 | |
-122 |
713 |
788 |
1400 |
|
14469 |
9608 |
8895 |
713 |
88 |
320,691,029,837 |
6 |
14 |
680 | |
14 |
984 |
1104 |
1890 |
|
17160 |
11922 |
10938 |
984 |
88 |
550,959,376,719 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3276 |
1625 |
1505 |
120 |
92 |
2,142,337,748 |
7 |
8 |
165 | |
105 |
166 |
166 |
175 |
|
4641 |
2373 |
2207 |
166 |
89 |
6,982,635,557 |
7 |
9 |
220 | |
51 |
224 |
224 |
260 |
|
6279 |
3322 |
3098 |
224 |
89 |
18,634,591,137 |
7 |
10 |
286 | |
-30 |
296 |
296 |
386 |
|
8190 |
4496 |
4200 |
296 |
87 |
45,467,497,121 |
7 |
11 |
364 | |
-126 |
384 |
384 |
564 |
|
10374 |
5919 |
5535 |
384 |
88 |
98,456,317,314 |
7 |
12 |
455 | |
-222 |
490 |
494 |
805 |
|
12831 |
7615 |
7125 |
490 |
87 |
201,965,343,493 |
7 |
13 |
560 | |
-294 |
616 |
643 |
1120 |
|
15561 |
9608 |
8992 |
616 |
87 |
386,636,424,094 |
7 |
14 |
680 | |
-318 |
779 |
851 |
1520 |
|
18564 |
11922 |
11143 |
779 |
88 |
714,449,910,337 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4680 |
2373 |
2208 |
165 |
90 |
7,140,351,065 |
8 |
9 |
220 | |
150 |
221 |
221 |
230 |
|
6396 |
3322 |
3101 |
221 |
90 |
19,395,349,758 |
8 |
10 |
286 | |
87 |
290 |
290 |
326 |
|
8424 |
4496 |
4206 |
290 |
88 |
48,108,882,728 |
8 |
11 |
364 | |
-12 |
374 |
374 |
464 |
|
10764 |
5919 |
5545 |
374 |
90 |
105,497,475,506 |
8 |
12 |
455 | |
-135 |
475 |
475 |
655 |
|
13416 |
7615 |
7140 |
475 |
89 |
221,796,989,513 |
8 |
13 |
560 | |
-270 |
595 |
595 |
910 |
|
16380 |
9608 |
9013 |
595 |
87 |
438,746,366,570 |
8 |
14 |
680 | |
-396 |
736 |
745 |
1240 |
|
19656 |
11922 |
11186 |
736 |
87 |
812,424,616,661 |
|
Bounds and Dimensions on generic Powell-Sabin
shelling parameters: a0 = 1 a1 = 10 a2 = 10 a3 = 3
Combinatorics:
24 | tetrahedra |
39 | interior faces |
19 | interior edges |
3 | interior vertices |
| |
18 | boundary faces |
27 | boundary edges |
11 | boundary vertices |
| |
57 | faces total |
46 | edges total |
14 | vertices total |