Bounds and Dimensions on aligned 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 |
6,025 |
1 |
2 |
10 | |
10 |
11 |
11 |
20 |
|
117 |
60 |
49 |
11 |
65 |
157,743 |
1 |
3 |
20 | |
34 |
38 |
38 |
60 |
|
234 |
163 |
125 |
38 |
56 |
871,273 |
1 |
4 |
35 | |
100 |
107 |
109 |
145 |
|
390 |
347 |
240 |
107 |
39 |
3,424,476 |
1 |
5 |
56 | |
232 |
242 |
248 |
296 |
|
585 |
636 |
394 |
242 |
30 |
11,241,699 |
1 |
6 |
84 | |
454 |
467 |
479 |
537 |
|
819 |
1036 |
587 |
449 |
24 |
27,358,910 |
1 |
7 |
120 | |
790 |
806 |
826 |
892 |
|
1092 |
1553 |
819 |
734 |
18 |
65,214,137 |
1 |
8 |
165 | |
1264 |
1283 |
1313 |
1385 |
|
1404 |
2187 |
1090 |
1097 |
19 |
125,447,096 |
1 |
9 |
220 | |
1900 |
1922 |
1964 |
2040 |
|
1755 |
2938 |
1400 |
1538 |
16 |
243,984,803 |
1 |
10 |
286 | |
2722 |
2747 |
2803 |
2881 |
|
2145 |
3806 |
1749 |
2057 |
17 |
406,536,802 |
1 |
11 |
364 | |
3754 |
3782 |
3854 |
3932 |
|
2574 |
4791 |
2137 |
2654 |
15 |
694,413,762 |
1 |
12 |
455 | |
5020 |
5051 |
5141 |
5217 |
|
3042 |
5893 |
2564 |
3329 |
16 |
1,052,630,409 |
1 |
13 |
560 | |
6544 |
6578 |
6688 |
6760 |
|
3549 |
7112 |
3030 |
4082 |
14 |
1,639,869,114 |
1 |
14 |
680 | |
8350 |
8387 |
8519 |
8585 |
|
4095 |
8448 |
3535 |
4913 |
15 |
2,383,303,729 |
1 |
15 |
816 | |
10462 |
10502 |
10658 |
10716 |
|
4680 |
9901 |
4079 |
5822 |
14 |
3,439,451,546 |
1 |
16 |
969 | |
12904 |
12947 |
13129 |
13177 |
|
5304 |
11471 |
4662 |
6809 |
14 |
4,653,886,411 |
1 |
17 |
1140 | |
15700 |
15746 |
15956 |
15992 |
|
5967 |
13158 |
5284 |
7874 |
13 |
6,534,538,363 |
1 |
18 |
1330 | |
18874 |
18923 |
19163 |
19185 |
|
6669 |
14962 |
5945 |
9017 |
14 |
8,524,350,499 |
1 |
19 |
1540 | |
22450 |
22502 |
22774 |
22780 |
|
7410 |
16883 |
6645 |
10238 |
13 |
11,521,801,631 |
1 |
20 |
1771 | |
26452 |
26507 |
26813 |
26801 |
|
8190 |
18921 |
7384 |
11537 |
14 |
14,627,026,996 |
1 |
21 |
2024 | |
30904 |
30962 |
31304 |
31272 |
|
9009 |
21076 |
8162 |
12914 |
13 |
19,176,380,959 |
1 |
22 |
2300 | |
35830 |
35891 |
36271 |
36217 |
|
9867 |
23348 |
8979 |
14369 |
13 |
23,772,243,318 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
156 |
60 |
50 |
10 |
75 |
202,569 |
2 |
3 |
20 | |
10 |
21 |
21 |
30 |
|
351 |
163 |
142 |
21 |
65 |
1,750,690 |
2 |
4 |
35 | |
16 |
44 |
44 |
75 |
|
624 |
347 |
303 |
44 |
60 |
8,555,216 |
2 |
5 |
56 | |
49 |
98 |
98 |
156 |
|
975 |
636 |
538 |
98 |
56 |
32,637,213 |
2 |
6 |
84 | |
133 |
204 |
206 |
294 |
|
1404 |
1054 |
850 |
204 |
52 |
93,146,520 |
2 |
7 |
120 | |
292 |
385 |
392 |
510 |
|
1911 |
1625 |
1240 |
385 |
45 |
245,343,048 |
2 |
8 |
165 | |
550 |
665 |
680 |
825 |
|
2496 |
2373 |
1708 |
665 |
42 |
569,482,513 |
2 |
9 |
220 | |
931 |
1068 |
1094 |
1263 |
|
3159 |
3304 |
2254 |
1050 |
30 |
1,123,394,745 |
2 |
10 |
286 | |
1459 |
1618 |
1658 |
1848 |
|
3900 |
4424 |
2878 |
1546 |
30 |
2,158,857,880 |
2 |
11 |
364 | |
2158 |
2339 |
2396 |
2604 |
|
4719 |
5739 |
3580 |
2159 |
24 |
3,960,856,025 |
2 |
12 |
455 | |
3052 |
3255 |
3332 |
3555 |
|
5616 |
7249 |
4360 |
2889 |
25 |
6,804,532,470 |
2 |
13 |
560 | |
4165 |
4390 |
4490 |
4725 |
|
6591 |
8954 |
5218 |
3736 |
21 |
10,396,613,451 |
2 |
14 |
680 | |
5521 |
5768 |
5894 |
6138 |
|
7644 |
10854 |
6154 |
4700 |
22 |
17,310,117,682 |
2 |
15 |
816 | |
7144 |
7413 |
7568 |
7818 |
|
8775 |
12949 |
7168 |
5781 |
19 |
25,107,054,719 |
2 |
16 |
969 | |
9058 |
9349 |
9536 |
9789 |
|
9984 |
15239 |
8260 |
6979 |
20 |
38,940,012,382 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
390 |
163 |
143 |
20 |
69 |
2,319,917 |
3 |
4 |
35 | |
15 |
36 |
36 |
45 |
|
741 |
347 |
311 |
36 |
67 |
13,462,009 |
3 |
5 |
56 | |
7 |
60 |
60 |
96 |
|
1209 |
636 |
576 |
60 |
75 |
66,207,394 |
3 |
6 |
84 | |
11 |
102 |
105 |
184 |
|
1794 |
1054 |
952 |
102 |
75 |
251,765,888 |
3 |
7 |
120 | |
51 |
184 |
190 |
320 |
|
2496 |
1625 |
1441 |
184 |
73 |
773,390,329 |
3 |
8 |
165 | |
151 |
328 |
339 |
525 |
|
3315 |
2373 |
2045 |
328 |
74 |
1,982,544,464 |
3 |
9 |
220 | |
335 |
556 |
576 |
820 |
|
4251 |
3322 |
2766 |
556 |
69 |
4,136,782,999 |
3 |
10 |
286 | |
627 |
892 |
925 |
1226 |
|
5304 |
4496 |
3604 |
892 |
64 |
8,081,083,735 |
3 |
11 |
364 | |
1051 |
1360 |
1410 |
1764 |
|
6474 |
5919 |
4559 |
1360 |
59 |
14,988,673,854 |
3 |
12 |
455 | |
1631 |
1984 |
2055 |
2458 |
|
7761 |
7597 |
5631 |
1966 |
55 |
25,986,039,190 |
3 |
13 |
560 | |
2391 |
2788 |
2884 |
3332 |
|
9165 |
9536 |
6820 |
2716 |
52 |
42,832,063,569 |
3 |
14 |
680 | |
3355 |
3796 |
3921 |
4410 |
|
10686 |
11742 |
8126 |
3616 |
49 |
67,595,140,615 |
3 |
15 |
816 | |
4547 |
5032 |
5190 |
5716 |
|
12324 |
14221 |
9549 |
4672 |
47 |
102,321,047,995 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
780 |
347 |
312 |
35 |
71 |
16,054,856 |
4 |
5 |
56 | |
26 |
57 |
57 |
66 |
|
1326 |
636 |
579 |
57 |
78 |
84,884,330 |
4 |
6 |
84 | |
5 |
88 |
88 |
124 |
|
2028 |
1054 |
966 |
88 |
78 |
356,043,283 |
4 |
7 |
120 | |
-16 |
134 |
134 |
220 |
|
2886 |
1625 |
1491 |
134 |
82 |
1,270,186,547 |
4 |
8 |
165 | |
-16 |
209 |
211 |
365 |
|
3900 |
2373 |
2164 |
209 |
83 |
3,540,326,554 |
4 |
9 |
220 | |
29 |
335 |
339 |
570 |
|
5070 |
3322 |
2987 |
335 |
83 |
8,406,287,430 |
4 |
10 |
286 | |
143 |
533 |
541 |
856 |
|
6396 |
4496 |
3963 |
533 |
83 |
18,297,786,680 |
4 |
11 |
364 | |
350 |
825 |
841 |
1244 |
|
7878 |
5919 |
5094 |
825 |
76 |
35,367,522,308 |
4 |
12 |
455 | |
674 |
1234 |
1263 |
1755 |
|
9516 |
7615 |
6381 |
1234 |
74 |
66,599,224,250 |
4 |
13 |
560 | |
1139 |
1784 |
1831 |
2410 |
|
11310 |
9608 |
7824 |
1784 |
68 |
112,329,499,735 |
4 |
14 |
680 | |
1769 |
2499 |
2569 |
3230 |
|
13260 |
11922 |
9423 |
2499 |
63 |
180,837,116,318 |
4 |
15 |
816 | |
2588 |
3403 |
3501 |
4239 |
|
15366 |
14563 |
11178 |
3385 |
58 |
288,050,661,343 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1365 |
636 |
580 |
56 |
79 |
95,356,803 |
5 |
6 |
84 | |
44 |
85 |
85 |
94 |
|
2145 |
1054 |
969 |
85 |
80 |
425,785,301 |
5 |
7 |
120 | |
11 |
124 |
124 |
160 |
|
3120 |
1625 |
1501 |
124 |
82 |
1,575,799,437 |
5 |
8 |
165 | |
-31 |
175 |
175 |
265 |
|
4290 |
2373 |
2198 |
175 |
80 |
4,767,505,864 |
5 |
9 |
220 | |
-67 |
248 |
248 |
420 |
|
5655 |
3322 |
3074 |
248 |
82 |
12,768,379,852 |
5 |
10 |
286 | |
-73 |
359 |
362 |
636 |
|
7215 |
4496 |
4137 |
359 |
84 |
29,029,449,904 |
5 |
11 |
364 | |
-25 |
530 |
536 |
924 |
|
8970 |
5919 |
5389 |
530 |
85 |
58,984,710,814 |
5 |
12 |
455 | |
101 |
783 |
794 |
1305 |
|
10920 |
7615 |
6832 |
783 |
85 |
114,316,988,544 |
5 |
13 |
560 | |
329 |
1140 |
1160 |
1800 |
|
13065 |
9608 |
8468 |
1140 |
84 |
204,016,839,679 |
5 |
14 |
680 | |
683 |
1623 |
1658 |
2430 |
|
15405 |
11922 |
10299 |
1623 |
82 |
343,346,818,293 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2184 |
1054 |
970 |
84 |
81 |
460,680,566 |
6 |
7 |
120 | |
70 |
121 |
121 |
130 |
|
3237 |
1625 |
1504 |
121 |
84 |
1,775,753,432 |
6 |
8 |
165 | |
26 |
169 |
169 |
205 |
|
4524 |
2373 |
2204 |
169 |
82 |
5,545,254,427 |
6 |
9 |
220 | |
-36 |
230 |
230 |
320 |
|
6045 |
3322 |
3092 |
230 |
82 |
15,661,922,066 |
6 |
10 |
286 | |
-104 |
310 |
310 |
486 |
|
7800 |
4496 |
4186 |
310 |
84 |
37,414,572,279 |
6 |
11 |
364 | |
-157 |
420 |
422 |
714 |
|
9789 |
5919 |
5499 |
420 |
85 |
78,854,730,644 |
6 |
12 |
455 | |
-171 |
578 |
585 |
1015 |
|
12012 |
7615 |
7037 |
578 |
87 |
157,301,056,846 |
6 |
13 |
560 | |
-122 |
807 |
819 |
1400 |
|
14469 |
9608 |
8801 |
807 |
89 |
281,154,150,542 |
6 |
14 |
680 | |
14 |
1128 |
1147 |
1890 |
|
17160 |
11922 |
10794 |
1128 |
89 |
486,962,969,104 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3276 |
1625 |
1505 |
120 |
85 |
1,836,340,423 |
7 |
8 |
165 | |
105 |
166 |
166 |
175 |
|
4641 |
2373 |
2207 |
166 |
84 |
5,992,799,282 |
7 |
9 |
220 | |
51 |
224 |
224 |
260 |
|
6279 |
3322 |
3098 |
224 |
82 |
16,802,588,591 |
7 |
10 |
286 | |
-30 |
296 |
296 |
386 |
|
8190 |
4496 |
4200 |
296 |
82 |
41,058,470,735 |
7 |
11 |
364 | |
-126 |
384 |
384 |
564 |
|
10374 |
5919 |
5535 |
384 |
83 |
90,464,647,066 |
7 |
12 |
455 | |
-222 |
498 |
498 |
805 |
|
12831 |
7615 |
7117 |
498 |
84 |
186,449,993,573 |
7 |
13 |
560 | |
-294 |
648 |
654 |
1120 |
|
15561 |
9608 |
8960 |
648 |
85 |
363,650,390,014 |
7 |
14 |
680 | |
-318 |
856 |
871 |
1520 |
|
18564 |
11922 |
11066 |
856 |
87 |
637,875,892,316 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4680 |
2373 |
2208 |
165 |
84 |
6,183,388,407 |
8 |
9 |
220 | |
150 |
221 |
221 |
230 |
|
6396 |
3322 |
3101 |
221 |
83 |
17,790,657,837 |
8 |
10 |
286 | |
87 |
290 |
290 |
326 |
|
8424 |
4496 |
4206 |
290 |
84 |
42,789,863,599 |
8 |
11 |
364 | |
-12 |
374 |
374 |
464 |
|
10764 |
5919 |
5545 |
374 |
85 |
99,187,864,403 |
8 |
12 |
455 | |
-135 |
475 |
475 |
655 |
|
13416 |
7615 |
7140 |
475 |
85 |
204,073,509,898 |
8 |
13 |
560 | |
-270 |
599 |
599 |
910 |
|
16380 |
9608 |
9009 |
599 |
84 |
397,520,284,145 |
8 |
14 |
680 | |
-396 |
756 |
756 |
1240 |
|
19656 |
11922 |
11166 |
756 |
86 |
741,301,361,497 |
|
Bounds and Dimensions on aligned 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 |