Bounds and Dimensions on the regular Worsey-Farin Split
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 |
|
18 |
9 |
5 |
4 |
100 |
1,262 |
1 |
2 |
10 | |
10 |
10 |
10 |
15 |
|
54 |
35 |
25 |
10 |
60 |
26,988 |
1 |
3 |
20 | |
28 |
28 |
28 |
40 |
|
108 |
91 |
63 |
28 |
38 |
133,498 |
1 |
4 |
35 | |
70 |
70 |
70 |
90 |
|
180 |
189 |
119 |
70 |
22 |
491,707 |
1 |
5 |
56 | |
148 |
148 |
148 |
176 |
|
270 |
341 |
193 |
148 |
26 |
1,561,575 |
1 |
6 |
84 | |
274 |
274 |
274 |
310 |
|
378 |
547 |
285 |
262 |
23 |
4,032,458 |
1 |
7 |
120 | |
460 |
460 |
460 |
504 |
|
504 |
807 |
395 |
412 |
23 |
9,643,435 |
1 |
8 |
165 | |
718 |
718 |
718 |
770 |
|
648 |
1121 |
523 |
598 |
22 |
19,431,464 |
1 |
9 |
220 | |
1060 |
1060 |
1060 |
1120 |
|
810 |
1489 |
669 |
820 |
21 |
37,464,407 |
1 |
10 |
286 | |
1498 |
1498 |
1498 |
1566 |
|
990 |
1911 |
833 |
1078 |
22 |
65,116,975 |
1 |
11 |
364 | |
2044 |
2044 |
2044 |
2120 |
|
1188 |
2387 |
1015 |
1372 |
21 |
109,255,744 |
1 |
12 |
455 | |
2710 |
2710 |
2710 |
2794 |
|
1404 |
2917 |
1215 |
1702 |
21 |
171,712,065 |
1 |
13 |
560 | |
3508 |
3508 |
3508 |
3600 |
|
1638 |
3501 |
1433 |
2068 |
21 |
269,323,754 |
1 |
14 |
680 | |
4450 |
4450 |
4450 |
4550 |
|
1890 |
4139 |
1669 |
2470 |
21 |
392,923,972 |
1 |
15 |
816 | |
5548 |
5548 |
5548 |
5656 |
|
2160 |
4831 |
1923 |
2908 |
21 |
577,011,978 |
1 |
16 |
969 | |
6814 |
6814 |
6814 |
6930 |
|
2448 |
5577 |
2195 |
3382 |
21 |
801,298,398 |
1 |
17 |
1140 | |
8260 |
8260 |
8260 |
8384 |
|
2754 |
6377 |
2485 |
3892 |
20 |
1,115,058,679 |
1 |
18 |
1330 | |
9898 |
9898 |
9898 |
10030 |
|
3078 |
7231 |
2793 |
4438 |
21 |
1,488,141,244 |
1 |
19 |
1540 | |
11740 |
11740 |
11740 |
11880 |
|
3420 |
8139 |
3119 |
5020 |
20 |
2,009,821,753 |
1 |
20 |
1771 | |
13798 |
13798 |
13798 |
13946 |
|
3780 |
9101 |
3463 |
5638 |
21 |
2,599,351,580 |
1 |
21 |
2024 | |
16084 |
16084 |
16084 |
16240 |
|
4158 |
10117 |
3825 |
6292 |
20 |
3,400,101,858 |
1 |
22 |
2300 | |
18610 |
18610 |
18610 |
18774 |
|
4554 |
11187 |
4205 |
6982 |
21 |
4,282,389,848 |
1 |
23 |
2600 | |
21388 |
21388 |
21388 |
21560 |
|
4968 |
12311 |
4603 |
7708 |
20 |
5,450,223,169 |
1 |
24 |
2925 | |
24430 |
24430 |
24430 |
24610 |
|
5400 |
13489 |
5019 |
8470 |
20 |
6,760,563,097 |
1 |
25 |
3276 | |
27748 |
27748 |
27748 |
27936 |
|
5850 |
14721 |
5453 |
9268 |
20 |
8,435,595,992 |
1 |
26 |
3654 | |
31354 |
31354 |
31354 |
31550 |
|
6318 |
16007 |
5905 |
10102 |
20 |
10,263,605,566 |
1 |
27 |
4060 | |
35260 |
35260 |
35260 |
35464 |
|
6804 |
17347 |
6375 |
10972 |
20 |
12,573,094,287 |
1 |
28 |
4495 | |
39478 |
39478 |
39478 |
39690 |
|
7308 |
18741 |
6863 |
11878 |
20 |
15,080,026,306 |
1 |
29 |
4960 | |
44020 |
44020 |
44020 |
44240 |
|
7830 |
20189 |
7369 |
12820 |
20 |
18,212,321,091 |
1 |
30 |
5456 | |
48898 |
48898 |
48898 |
49126 |
|
8370 |
21691 |
7893 |
13798 |
20 |
21,522,179,678 |
1 |
31 |
5984 | |
54124 |
54124 |
54124 |
54360 |
|
8928 |
23247 |
8435 |
14812 |
20 |
25,768,765,363 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
72 |
35 |
25 |
10 |
60 |
36,309 |
2 |
3 |
20 | |
15 |
20 |
20 |
25 |
|
162 |
91 |
71 |
20 |
43 |
304,687 |
2 |
4 |
35 | |
27 |
39 |
39 |
55 |
|
288 |
189 |
150 |
39 |
44 |
1,480,118 |
2 |
5 |
56 | |
57 |
77 |
77 |
106 |
|
450 |
341 |
264 |
77 |
35 |
5,275,544 |
2 |
6 |
84 | |
117 |
145 |
145 |
189 |
|
648 |
559 |
414 |
145 |
30 |
14,247,707 |
2 |
7 |
120 | |
219 |
255 |
255 |
315 |
|
882 |
855 |
600 |
255 |
25 |
34,889,782 |
2 |
8 |
165 | |
375 |
419 |
419 |
495 |
|
1152 |
1241 |
822 |
419 |
24 |
76,333,917 |
2 |
9 |
220 | |
597 |
649 |
649 |
741 |
|
1458 |
1717 |
1080 |
637 |
20 |
149,725,628 |
2 |
10 |
286 | |
897 |
957 |
957 |
1065 |
|
1800 |
2283 |
1374 |
909 |
20 |
271,216,046 |
2 |
11 |
364 | |
1287 |
1355 |
1355 |
1479 |
|
2178 |
2939 |
1704 |
1235 |
18 |
467,327,881 |
2 |
12 |
455 | |
1779 |
1855 |
1855 |
1995 |
|
2592 |
3685 |
2070 |
1615 |
18 |
769,999,237 |
2 |
13 |
560 | |
2385 |
2469 |
2469 |
2625 |
|
3042 |
4521 |
2472 |
2049 |
17 |
1,218,389,859 |
2 |
14 |
680 | |
3117 |
3209 |
3209 |
3381 |
|
3528 |
5447 |
2910 |
2537 |
17 |
1,825,711,376 |
2 |
15 |
816 | |
3987 |
4087 |
4087 |
4275 |
|
4050 |
6463 |
3384 |
3079 |
16 |
2,669,673,320 |
2 |
16 |
969 | |
5007 |
5115 |
5115 |
5319 |
|
4608 |
7569 |
3894 |
3675 |
17 |
3,844,057,319 |
2 |
17 |
1140 | |
6189 |
6305 |
6305 |
6525 |
|
5202 |
8765 |
4440 |
4325 |
16 |
5,477,009,923 |
2 |
18 |
1330 | |
7545 |
7669 |
7669 |
7905 |
|
5832 |
10051 |
5022 |
5029 |
16 |
7,512,938,611 |
2 |
19 |
1540 | |
9087 |
9219 |
9219 |
9471 |
|
6498 |
11427 |
5640 |
5787 |
15 |
10,250,492,582 |
2 |
20 |
1771 | |
10827 |
10967 |
10967 |
11235 |
|
7200 |
12893 |
6294 |
6599 |
16 |
13,402,746,477 |
2 |
21 |
2024 | |
12777 |
12925 |
12925 |
13209 |
|
7938 |
14449 |
6984 |
7465 |
15 |
17,695,057,258 |
2 |
22 |
2300 | |
14949 |
15105 |
15105 |
15405 |
|
8712 |
16095 |
7710 |
8385 |
15 |
23,093,663,878 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
180 |
91 |
71 |
20 |
43 |
417,892 |
3 |
4 |
35 | |
25 |
35 |
35 |
40 |
|
342 |
189 |
154 |
35 |
41 |
2,416,929 |
3 |
5 |
56 | |
33 |
56 |
56 |
76 |
|
558 |
341 |
285 |
56 |
51 |
11,611,155 |
3 |
6 |
84 | |
53 |
92 |
92 |
134 |
|
828 |
559 |
467 |
92 |
58 |
38,417,193 |
3 |
7 |
120 | |
97 |
152 |
152 |
220 |
|
1152 |
855 |
703 |
152 |
69 |
99,627,815 |
3 |
8 |
165 | |
177 |
248 |
248 |
345 |
|
1530 |
1241 |
993 |
248 |
68 |
217,973,598 |
3 |
9 |
220 | |
305 |
392 |
392 |
520 |
|
1962 |
1729 |
1337 |
392 |
63 |
473,546,568 |
3 |
10 |
286 | |
493 |
596 |
596 |
756 |
|
2448 |
2331 |
1735 |
596 |
60 |
922,149,927 |
3 |
11 |
364 | |
753 |
872 |
872 |
1064 |
|
2988 |
3059 |
2187 |
872 |
56 |
1,552,578,031 |
3 |
12 |
455 | |
1097 |
1232 |
1232 |
1456 |
|
3582 |
3913 |
2693 |
1220 |
54 |
2,818,978,114 |
3 |
13 |
560 | |
1537 |
1688 |
1688 |
1944 |
|
4230 |
4893 |
3253 |
1640 |
52 |
4,150,591,530 |
3 |
14 |
680 | |
2085 |
2252 |
2252 |
2540 |
|
4932 |
5999 |
3867 |
2132 |
50 |
6,815,961,832 |
3 |
15 |
816 | |
2753 |
2936 |
2936 |
3256 |
|
5688 |
7231 |
4535 |
2696 |
50 |
9,646,467,193 |
3 |
16 |
969 | |
3553 |
3752 |
3752 |
4104 |
|
6498 |
8589 |
5257 |
3332 |
49 |
14,384,191,284 |
3 |
17 |
1140 | |
4497 |
4712 |
4712 |
5096 |
|
7362 |
10073 |
6033 |
4040 |
48 |
21,428,466,063 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
360 |
189 |
154 |
35 |
41 |
3,234,072 |
4 |
5 |
56 | |
41 |
56 |
56 |
61 |
|
612 |
341 |
285 |
56 |
51 |
16,047,141 |
4 |
6 |
84 | |
46 |
84 |
84 |
104 |
|
936 |
559 |
475 |
84 |
60 |
60,539,374 |
4 |
7 |
120 | |
58 |
124 |
124 |
170 |
|
1332 |
855 |
731 |
124 |
70 |
201,718,660 |
4 |
8 |
165 | |
88 |
185 |
185 |
265 |
|
1800 |
1241 |
1056 |
185 |
76 |
485,353,649 |
4 |
9 |
220 | |
148 |
277 |
277 |
395 |
|
2340 |
1729 |
1452 |
277 |
74 |
1,060,299,582 |
4 |
10 |
286 | |
250 |
411 |
411 |
571 |
|
2952 |
2331 |
1920 |
411 |
77 |
2,188,585,566 |
4 |
11 |
364 | |
406 |
599 |
599 |
804 |
|
3636 |
3059 |
2460 |
599 |
70 |
4,274,782,463 |
4 |
12 |
455 | |
628 |
853 |
853 |
1105 |
|
4392 |
3925 |
3072 |
853 |
69 |
7,618,918,836 |
4 |
13 |
560 | |
928 |
1185 |
1185 |
1485 |
|
5220 |
4941 |
3756 |
1185 |
62 |
12,093,837,055 |
4 |
14 |
680 | |
1318 |
1607 |
1607 |
1955 |
|
6120 |
6119 |
4512 |
1607 |
60 |
20,116,701,720 |
4 |
15 |
816 | |
1810 |
2131 |
2131 |
2527 |
|
7092 |
7459 |
5340 |
2119 |
56 |
31,495,787,968 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
630 |
341 |
285 |
56 |
51 |
19,153,371 |
5 |
6 |
84 | |
64 |
84 |
84 |
89 |
|
990 |
559 |
475 |
84 |
60 |
74,766,064 |
5 |
7 |
120 | |
67 |
120 |
120 |
140 |
|
1440 |
855 |
735 |
120 |
66 |
257,034,153 |
5 |
8 |
165 | |
73 |
165 |
165 |
215 |
|
1980 |
1241 |
1076 |
165 |
70 |
735,050,825 |
5 |
9 |
220 | |
91 |
228 |
228 |
320 |
|
2610 |
1729 |
1501 |
228 |
74 |
1,780,016,729 |
5 |
10 |
286 | |
133 |
318 |
318 |
461 |
|
3330 |
2331 |
2013 |
318 |
78 |
3,790,062,803 |
5 |
11 |
364 | |
211 |
444 |
444 |
644 |
|
4140 |
3059 |
2615 |
444 |
81 |
7,124,666,538 |
5 |
12 |
455 | |
337 |
618 |
618 |
880 |
|
5040 |
3925 |
3307 |
618 |
84 |
12,684,664,639 |
5 |
13 |
560 | |
523 |
852 |
852 |
1180 |
|
6030 |
4941 |
4089 |
852 |
84 |
23,188,174,861 |
5 |
14 |
680 | |
781 |
1158 |
1158 |
1555 |
|
7110 |
6119 |
4961 |
1158 |
84 |
35,737,028,837 |
5 |
15 |
816 | |
1123 |
1548 |
1548 |
2016 |
|
8280 |
7471 |
5923 |
1548 |
82 |
57,094,961,268 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
1008 |
559 |
475 |
84 |
60 |
84,417,961 |
6 |
7 |
120 | |
95 |
120 |
120 |
125 |
|
1494 |
855 |
735 |
120 |
66 |
291,667,443 |
6 |
8 |
165 | |
97 |
165 |
165 |
185 |
|
2088 |
1241 |
1076 |
165 |
70 |
856,586,729 |
6 |
9 |
220 | |
98 |
220 |
220 |
270 |
|
2790 |
1729 |
1509 |
220 |
72 |
2,155,405,673 |
6 |
10 |
286 | |
106 |
290 |
290 |
386 |
|
3600 |
2331 |
2041 |
290 |
74 |
4,926,954,103 |
6 |
11 |
364 | |
132 |
384 |
384 |
539 |
|
4518 |
3059 |
2675 |
384 |
78 |
10,418,241,678 |
6 |
12 |
455 | |
188 |
511 |
511 |
735 |
|
5544 |
3925 |
3414 |
511 |
82 |
19,651,380,112 |
6 |
13 |
560 | |
286 |
681 |
681 |
980 |
|
6678 |
4941 |
4260 |
681 |
83 |
34,926,842,855 |
6 |
14 |
680 | |
438 |
905 |
905 |
1285 |
|
7920 |
6119 |
5214 |
905 |
84 |
56,890,569,211 |
6 |
15 |
816 | |
656 |
1195 |
1195 |
1661 |
|
9270 |
7471 |
6276 |
1195 |
84 |
93,497,828,498 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
1512 |
855 |
735 |
120 |
66 |
313,082,010 |
7 |
8 |
165 | |
135 |
165 |
165 |
170 |
|
2142 |
1241 |
1076 |
165 |
70 |
940,074,917 |
7 |
9 |
220 | |
137 |
220 |
220 |
240 |
|
2898 |
1729 |
1509 |
220 |
72 |
2,441,869,754 |
7 |
10 |
286 | |
134 |
286 |
286 |
336 |
|
3780 |
2331 |
2045 |
286 |
73 |
5,764,179,600 |
7 |
11 |
364 | |
134 |
364 |
364 |
464 |
|
4788 |
3059 |
2695 |
364 |
76 |
12,291,236,312 |
7 |
12 |
455 | |
146 |
463 |
463 |
630 |
|
5922 |
3925 |
3462 |
463 |
79 |
24,728,767,829 |
7 |
13 |
560 | |
182 |
592 |
592 |
840 |
|
7182 |
4941 |
4349 |
592 |
82 |
45,900,914,956 |
7 |
14 |
680 | |
254 |
760 |
760 |
1100 |
|
8568 |
6119 |
5359 |
760 |
84 |
79,848,849,428 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
2160 |
1241 |
1076 |
165 |
70 |
979,602,677 |
8 |
9 |
220 | |
185 |
220 |
220 |
225 |
|
2952 |
1729 |
1509 |
220 |
72 |
2,630,828,906 |
8 |
10 |
286 | |
188 |
286 |
286 |
306 |
|
3888 |
2331 |
2045 |
286 |
73 |
6,153,430,995 |
8 |
11 |
364 | |
182 |
364 |
364 |
414 |
|
4968 |
3059 |
2695 |
364 |
76 |
13,746,829,658 |
8 |
12 |
455 | |
175 |
455 |
455 |
555 |
|
6192 |
3925 |
3470 |
455 |
79 |
28,606,627,311 |
8 |
13 |
560 | |
175 |
564 |
564 |
735 |
|
7560 |
4941 |
4377 |
564 |
79 |
55,757,373,465 |
8 |
14 |
680 | |
193 |
700 |
700 |
960 |
|
9072 |
6119 |
5419 |
700 |
82 |
102,400,744,136 |
|
Bounds and Dimensions on the regular Worsey-Farin Split
shelling parameters: a0 = 1 a1 = 5 a2 = 5 a3 = 1
Combinatorics:
12 | tetrahedra |
18 | interior faces |
8 | interior edges |
1 | interior vertices |
| |
12 | boundary faces |
18 | boundary edges |
8 | boundary vertices |
| |
30 | faces total |
26 | edges total |
9 | vertices total |