Bounds and Dimensions on unaligned 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 |
6,133 |
1 |
2 |
10 | |
10 |
11 |
11 |
20 |
|
117 |
60 |
49 |
11 |
71 |
161,972 |
1 |
3 |
20 | |
34 |
38 |
38 |
60 |
|
234 |
163 |
125 |
38 |
69 |
920,890 |
1 |
4 |
35 | |
100 |
107 |
109 |
145 |
|
390 |
347 |
240 |
107 |
49 |
3,697,562 |
1 |
5 |
56 | |
232 |
242 |
248 |
296 |
|
585 |
636 |
394 |
242 |
32 |
12,033,515 |
1 |
6 |
84 | |
454 |
467 |
479 |
537 |
|
819 |
1036 |
587 |
449 |
27 |
30,463,255 |
1 |
7 |
120 | |
790 |
806 |
826 |
892 |
|
1092 |
1553 |
819 |
734 |
23 |
71,316,158 |
1 |
8 |
165 | |
1264 |
1283 |
1313 |
1385 |
|
1404 |
2187 |
1090 |
1097 |
21 |
140,713,441 |
1 |
9 |
220 | |
1900 |
1922 |
1964 |
2040 |
|
1755 |
2938 |
1400 |
1538 |
19 |
269,756,718 |
1 |
10 |
286 | |
2722 |
2747 |
2803 |
2881 |
|
2145 |
3806 |
1749 |
2057 |
18 |
456,469,247 |
1 |
11 |
364 | |
3754 |
3782 |
3854 |
3932 |
|
2574 |
4791 |
2137 |
2654 |
17 |
770,504,519 |
1 |
12 |
455 | |
5020 |
5051 |
5141 |
5217 |
|
3042 |
5893 |
2564 |
3329 |
17 |
1,186,382,741 |
1 |
13 |
560 | |
6544 |
6578 |
6688 |
6760 |
|
3549 |
7112 |
3030 |
4082 |
16 |
1,835,218,933 |
1 |
14 |
680 | |
8350 |
8387 |
8519 |
8585 |
|
4095 |
8448 |
3535 |
4913 |
16 |
2,709,263,576 |
1 |
15 |
816 | |
10462 |
10502 |
10658 |
10716 |
|
4680 |
9901 |
4079 |
5822 |
16 |
3,846,621,294 |
1 |
16 |
969 | |
12904 |
12947 |
13129 |
13177 |
|
5304 |
11471 |
4662 |
6809 |
15 |
5,275,414,375 |
1 |
17 |
1140 | |
15700 |
15746 |
15956 |
15992 |
|
5967 |
13158 |
5284 |
7874 |
15 |
7,326,826,346 |
1 |
18 |
1330 | |
18874 |
18923 |
19163 |
19185 |
|
6669 |
14962 |
5945 |
9017 |
15 |
9,656,300,056 |
1 |
19 |
1540 | |
22450 |
22502 |
22774 |
22780 |
|
7410 |
16883 |
6645 |
10238 |
15 |
12,942,416,208 |
1 |
20 |
1771 | |
26452 |
26507 |
26813 |
26801 |
|
8190 |
18921 |
7384 |
11537 |
14 |
16,610,948,226 |
1 |
21 |
2024 | |
30904 |
30962 |
31304 |
31272 |
|
9009 |
21076 |
8162 |
12914 |
14 |
21,575,182,580 |
1 |
22 |
2300 | |
35830 |
35891 |
36271 |
36217 |
|
9867 |
23348 |
8979 |
14369 |
14 |
27,022,059,904 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
156 |
60 |
50 |
10 |
80 |
207,967 |
2 |
3 |
20 | |
10 |
21 |
21 |
30 |
|
351 |
163 |
142 |
21 |
75 |
1,826,530 |
2 |
4 |
35 | |
16 |
44 |
44 |
75 |
|
624 |
347 |
303 |
44 |
78 |
8,753,552 |
2 |
5 |
56 | |
49 |
97 |
98 |
156 |
|
975 |
636 |
539 |
97 |
66 |
33,435,078 |
2 |
6 |
84 | |
133 |
202 |
206 |
294 |
|
1404 |
1054 |
852 |
202 |
54 |
99,864,439 |
2 |
7 |
120 | |
292 |
382 |
392 |
510 |
|
1911 |
1625 |
1243 |
382 |
49 |
262,615,243 |
2 |
8 |
165 | |
550 |
661 |
680 |
825 |
|
2496 |
2373 |
1712 |
661 |
46 |
633,314,959 |
2 |
9 |
220 | |
931 |
1063 |
1094 |
1263 |
|
3159 |
3304 |
2259 |
1045 |
38 |
1,249,195,136 |
2 |
10 |
286 | |
1459 |
1612 |
1658 |
1848 |
|
3900 |
4424 |
2884 |
1540 |
33 |
2,428,831,737 |
2 |
11 |
364 | |
2158 |
2332 |
2396 |
2604 |
|
4719 |
5739 |
3587 |
2152 |
30 |
4,444,587,958 |
2 |
12 |
455 | |
3052 |
3247 |
3332 |
3555 |
|
5616 |
7249 |
4368 |
2881 |
27 |
7,664,773,646 |
2 |
13 |
560 | |
4165 |
4381 |
4490 |
4725 |
|
6591 |
8954 |
5227 |
3727 |
25 |
11,668,724,688 |
2 |
14 |
680 | |
5521 |
5758 |
5894 |
6138 |
|
7644 |
10854 |
6164 |
4690 |
24 |
19,545,434,529 |
2 |
15 |
816 | |
7144 |
7402 |
7568 |
7818 |
|
8775 |
12949 |
7179 |
5770 |
23 |
28,316,610,310 |
2 |
16 |
969 | |
9058 |
9337 |
9536 |
9789 |
|
9984 |
15239 |
8272 |
6967 |
22 |
44,210,814,215 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
390 |
163 |
143 |
20 |
80 |
2,396,834 |
3 |
4 |
35 | |
15 |
36 |
36 |
45 |
|
741 |
347 |
311 |
36 |
83 |
13,584,689 |
3 |
5 |
56 | |
7 |
60 |
60 |
96 |
|
1209 |
636 |
576 |
60 |
82 |
66,533,497 |
3 |
6 |
84 | |
11 |
100 |
105 |
184 |
|
1794 |
1054 |
954 |
100 |
76 |
254,215,261 |
3 |
7 |
120 | |
51 |
180 |
190 |
320 |
|
2496 |
1625 |
1445 |
180 |
73 |
767,114,216 |
3 |
8 |
165 | |
151 |
322 |
339 |
525 |
|
3315 |
2373 |
2051 |
322 |
71 |
1,986,782,134 |
3 |
9 |
220 | |
335 |
548 |
576 |
820 |
|
4251 |
3322 |
2774 |
548 |
65 |
4,153,788,758 |
3 |
10 |
286 | |
627 |
882 |
925 |
1226 |
|
5304 |
4496 |
3614 |
882 |
60 |
8,224,134,533 |
3 |
11 |
364 | |
1051 |
1348 |
1410 |
1764 |
|
6474 |
5919 |
4571 |
1348 |
55 |
15,149,360,797 |
3 |
12 |
455 | |
1631 |
1970 |
2055 |
2458 |
|
7761 |
7597 |
5645 |
1952 |
51 |
26,285,552,948 |
3 |
13 |
560 | |
2391 |
2772 |
2884 |
3332 |
|
9165 |
9536 |
6836 |
2700 |
49 |
43,377,463,520 |
3 |
14 |
680 | |
3355 |
3778 |
3921 |
4410 |
|
10686 |
11742 |
8144 |
3598 |
46 |
69,350,020,061 |
3 |
15 |
816 | |
4547 |
5012 |
5190 |
5716 |
|
12324 |
14221 |
9569 |
4652 |
45 |
106,562,647,297 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
780 |
347 |
312 |
35 |
86 |
16,224,143 |
4 |
5 |
56 | |
26 |
57 |
57 |
66 |
|
1326 |
636 |
579 |
57 |
85 |
84,541,997 |
4 |
6 |
84 | |
5 |
88 |
88 |
124 |
|
2028 |
1054 |
966 |
88 |
87 |
360,174,343 |
4 |
7 |
120 | |
-16 |
133 |
133 |
220 |
|
2886 |
1625 |
1492 |
133 |
88 |
1,288,369,252 |
4 |
8 |
165 | |
-16 |
202 |
209 |
365 |
|
3900 |
2373 |
2171 |
202 |
88 |
3,541,679,336 |
4 |
9 |
220 | |
29 |
321 |
336 |
570 |
|
5070 |
3322 |
3001 |
321 |
89 |
8,420,111,404 |
4 |
10 |
286 | |
143 |
512 |
537 |
856 |
|
6396 |
4496 |
3984 |
512 |
86 |
18,370,112,353 |
4 |
11 |
364 | |
350 |
797 |
836 |
1244 |
|
7878 |
5919 |
5122 |
797 |
81 |
35,702,197,205 |
4 |
12 |
455 | |
674 |
1199 |
1257 |
1755 |
|
9516 |
7615 |
6416 |
1199 |
74 |
67,185,505,274 |
4 |
13 |
560 | |
1139 |
1742 |
1824 |
2410 |
|
11310 |
9608 |
7866 |
1742 |
68 |
113,638,721,871 |
4 |
14 |
680 | |
1769 |
2450 |
2561 |
3230 |
|
13260 |
11922 |
9472 |
2450 |
62 |
182,129,021,530 |
4 |
15 |
816 | |
2588 |
3347 |
3492 |
4239 |
|
15366 |
14563 |
11234 |
3329 |
57 |
292,179,877,480 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1365 |
636 |
580 |
56 |
87 |
95,698,890 |
5 |
6 |
84 | |
44 |
85 |
85 |
94 |
|
2145 |
1054 |
969 |
85 |
90 |
429,078,757 |
5 |
7 |
120 | |
11 |
124 |
124 |
160 |
|
3120 |
1625 |
1501 |
124 |
92 |
1,586,721,955 |
5 |
8 |
165 | |
-31 |
175 |
175 |
265 |
|
4290 |
2373 |
2198 |
175 |
88 |
4,816,666,856 |
5 |
9 |
220 | |
-67 |
246 |
248 |
420 |
|
5655 |
3322 |
3076 |
246 |
88 |
12,762,125,212 |
5 |
10 |
286 | |
-73 |
349 |
362 |
636 |
|
7215 |
4496 |
4147 |
349 |
87 |
29,138,165,117 |
5 |
11 |
364 | |
-25 |
512 |
536 |
924 |
|
8970 |
5919 |
5407 |
512 |
86 |
59,169,619,482 |
5 |
12 |
455 | |
101 |
757 |
794 |
1305 |
|
10920 |
7615 |
6858 |
757 |
85 |
114,432,506,038 |
5 |
13 |
560 | |
329 |
1106 |
1160 |
1800 |
|
13065 |
9608 |
8502 |
1106 |
84 |
204,799,095,830 |
5 |
14 |
680 | |
683 |
1581 |
1658 |
2430 |
|
15405 |
11922 |
10341 |
1581 |
80 |
345,940,428,976 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2184 |
1054 |
970 |
84 |
91 |
463,381,306 |
6 |
7 |
120 | |
70 |
121 |
121 |
130 |
|
3237 |
1625 |
1504 |
121 |
94 |
1,789,116,516 |
6 |
8 |
165 | |
26 |
169 |
169 |
205 |
|
4524 |
2373 |
2204 |
169 |
90 |
5,608,219,054 |
6 |
9 |
220 | |
-36 |
230 |
230 |
320 |
|
6045 |
3322 |
3092 |
230 |
89 |
15,716,253,270 |
6 |
10 |
286 | |
-104 |
309 |
309 |
486 |
|
7800 |
4496 |
4187 |
309 |
88 |
37,575,605,540 |
6 |
11 |
364 | |
-157 |
414 |
420 |
714 |
|
9789 |
5919 |
5505 |
414 |
88 |
79,370,483,223 |
6 |
12 |
455 | |
-171 |
562 |
582 |
1015 |
|
12012 |
7615 |
7053 |
562 |
90 |
156,719,345,819 |
6 |
13 |
560 | |
-122 |
781 |
815 |
1400 |
|
14469 |
9608 |
8827 |
781 |
91 |
280,547,148,783 |
6 |
14 |
680 | |
14 |
1092 |
1142 |
1890 |
|
17160 |
11922 |
10830 |
1092 |
89 |
486,770,457,813 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3276 |
1625 |
1505 |
120 |
95 |
1,859,594,836 |
7 |
8 |
165 | |
105 |
166 |
166 |
175 |
|
4641 |
2373 |
2207 |
166 |
92 |
6,059,571,337 |
7 |
9 |
220 | |
51 |
224 |
224 |
260 |
|
6279 |
3322 |
3098 |
224 |
91 |
16,959,891,483 |
7 |
10 |
286 | |
-30 |
296 |
296 |
386 |
|
8190 |
4496 |
4200 |
296 |
90 |
41,368,618,374 |
7 |
11 |
364 | |
-126 |
384 |
384 |
564 |
|
10374 |
5919 |
5535 |
384 |
89 |
91,388,822,235 |
7 |
12 |
455 | |
-222 |
496 |
496 |
805 |
|
12831 |
7615 |
7119 |
496 |
90 |
187,745,616,334 |
7 |
13 |
560 | |
-294 |
640 |
650 |
1120 |
|
15561 |
9608 |
8968 |
640 |
89 |
365,386,263,311 |
7 |
14 |
680 | |
-318 |
836 |
865 |
1520 |
|
18564 |
11922 |
11086 |
836 |
90 |
645,256,200,594 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4680 |
2373 |
2208 |
165 |
93 |
6,222,276,441 |
8 |
9 |
220 | |
150 |
221 |
221 |
230 |
|
6396 |
3322 |
3101 |
221 |
92 |
17,898,901,074 |
8 |
10 |
286 | |
87 |
290 |
290 |
326 |
|
8424 |
4496 |
4206 |
290 |
91 |
43,470,195,634 |
8 |
11 |
364 | |
-12 |
374 |
374 |
464 |
|
10764 |
5919 |
5545 |
374 |
91 |
100,645,381,803 |
8 |
12 |
455 | |
-135 |
475 |
475 |
655 |
|
13416 |
7615 |
7140 |
475 |
91 |
205,870,787,643 |
8 |
13 |
560 | |
-270 |
598 |
598 |
910 |
|
16380 |
9608 |
9010 |
598 |
89 |
402,852,611,101 |
8 |
14 |
680 | |
-396 |
751 |
754 |
1240 |
|
19656 |
11922 |
11171 |
751 |
88 |
749,674,854,415 |
|
Bounds and Dimensions on unaligned 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 |