Bounds and Dimensions on generic MS cone
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 |
|
9 |
7 |
3 |
4 |
75 |
411 |
1 |
2 |
10 | |
10 |
10 |
11 |
13 |
|
27 |
25 |
15 |
10 |
40 |
8,619 |
1 |
3 |
20 | |
26 |
26 |
29 |
32 |
|
54 |
62 |
36 |
26 |
26 |
29,601 |
1 |
4 |
35 | |
59 |
59 |
65 |
68 |
|
90 |
122 |
66 |
56 |
18 |
79,677 |
1 |
5 |
56 | |
116 |
116 |
126 |
128 |
|
135 |
209 |
105 |
104 |
14 |
186,963 |
1 |
6 |
84 | |
204 |
204 |
219 |
219 |
|
189 |
323 |
153 |
170 |
11 |
382,614 |
1 |
7 |
120 | |
330 |
330 |
351 |
348 |
|
252 |
464 |
210 |
254 |
9 |
708,783 |
1 |
8 |
165 | |
501 |
501 |
529 |
522 |
|
324 |
632 |
276 |
356 |
7 |
1,214,217 |
1 |
9 |
220 | |
724 |
724 |
760 |
748 |
|
405 |
827 |
351 |
476 |
6 |
1,955,439 |
1 |
10 |
286 | |
1006 |
1006 |
1051 |
1033 |
|
495 |
1049 |
435 |
614 |
6 |
2,996,748 |
1 |
11 |
364 | |
1354 |
1354 |
1409 |
1384 |
|
594 |
1298 |
528 |
770 |
5 |
4,410,219 |
1 |
12 |
455 | |
1775 |
1775 |
1841 |
1808 |
|
702 |
1574 |
630 |
944 |
4 |
6,275,703 |
1 |
13 |
560 | |
2276 |
2276 |
2354 |
2312 |
|
819 |
1877 |
741 |
1136 |
4 |
8,680,827 |
1 |
14 |
680 | |
2864 |
2864 |
2955 |
2903 |
|
945 |
2207 |
861 |
1346 |
4 |
11,720,994 |
1 |
15 |
816 | |
3546 |
3546 |
3651 |
3588 |
|
1080 |
2564 |
990 |
1574 |
3 |
15,499,383 |
1 |
16 |
969 | |
4329 |
4329 |
4449 |
4374 |
|
1224 |
2948 |
1128 |
1820 |
3 |
20,126,949 |
1 |
17 |
1140 | |
5220 |
5220 |
5356 |
5268 |
|
1377 |
3359 |
1275 |
2084 |
3 |
25,722,423 |
1 |
18 |
1330 | |
6226 |
6226 |
6379 |
6277 |
|
1539 |
3797 |
1431 |
2366 |
3 |
32,412,312 |
1 |
19 |
1540 | |
7354 |
7354 |
7525 |
7408 |
|
1710 |
4262 |
1596 |
2666 |
2 |
40,330,899 |
1 |
20 |
1771 | |
8611 |
8611 |
8801 |
8668 |
|
1890 |
4754 |
1770 |
2984 |
2 |
49,620,243 |
1 |
21 |
2024 | |
10004 |
10004 |
10214 |
10064 |
|
2079 |
5273 |
1953 |
3320 |
2 |
60,430,179 |
1 |
22 |
2300 | |
11540 |
11540 |
11771 |
11603 |
|
2277 |
5819 |
2145 |
3674 |
2 |
72,918,318 |
1 |
23 |
2600 | |
13226 |
13226 |
13479 |
13292 |
|
2484 |
6392 |
2346 |
4046 |
2 |
87,250,047 |
1 |
24 |
2925 | |
15069 |
15069 |
15345 |
15138 |
|
2700 |
6992 |
2556 |
4436 |
2 |
103,598,529 |
1 |
25 |
3276 | |
17076 |
17076 |
17376 |
17148 |
|
2925 |
7619 |
2775 |
4844 |
2 |
122,144,703 |
1 |
26 |
3654 | |
19254 |
19254 |
19579 |
19329 |
|
3159 |
8273 |
3003 |
5270 |
2 |
143,077,284 |
1 |
27 |
4060 | |
21610 |
21610 |
21961 |
21688 |
|
3402 |
8954 |
3240 |
5714 |
1 |
166,592,763 |
1 |
28 |
4495 | |
24151 |
24151 |
24529 |
24232 |
|
3654 |
9662 |
3486 |
6176 |
1 |
192,895,407 |
1 |
29 |
4960 | |
26884 |
26884 |
27290 |
26968 |
|
3915 |
10397 |
3741 |
6656 |
1 |
222,197,259 |
1 |
30 |
5456 | |
29816 |
29816 |
30251 |
29903 |
|
4185 |
11159 |
4005 |
7154 |
1 |
254,718,138 |
1 |
31 |
5984 | |
32954 |
32954 |
33419 |
33044 |
|
4464 |
11948 |
4278 |
7670 |
1 |
290,685,639 |
1 |
32 |
6545 | |
36305 |
36305 |
36801 |
36398 |
|
4752 |
12764 |
4560 |
8204 |
1 |
330,335,133 |
1 |
33 |
7140 | |
39876 |
39876 |
40404 |
39972 |
|
5049 |
13607 |
4851 |
8756 |
1 |
373,909,767 |
1 |
34 |
7770 | |
43674 |
43674 |
44235 |
43773 |
|
5355 |
14477 |
5151 |
9326 |
1 |
421,660,464 |
1 |
35 |
8436 | |
47706 |
47706 |
48301 |
47808 |
|
5670 |
15374 |
5460 |
9914 |
1 |
473,845,923 |
1 |
36 |
9139 | |
51979 |
51979 |
52609 |
52084 |
|
5994 |
16298 |
5778 |
10520 |
1 |
530,732,619 |
1 |
37 |
9880 | |
56500 |
56500 |
57166 |
56608 |
|
6327 |
17249 |
6105 |
11144 |
1 |
592,594,803 |
1 |
38 |
10660 | |
61276 |
61276 |
61979 |
61387 |
|
6669 |
18227 |
6441 |
11786 |
1 |
659,714,502 |
1 |
39 |
11480 | |
66314 |
66314 |
67055 |
66428 |
|
7020 |
19232 |
6786 |
12446 |
1 |
732,381,519 |
1 |
40 |
12341 | |
71621 |
71621 |
72401 |
71738 |
|
7380 |
20264 |
7140 |
13124 |
1 |
810,893,433 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
36 |
25 |
15 |
10 |
40 |
8,367 |
2 |
3 |
20 | |
17 |
20 |
20 |
23 |
|
81 |
62 |
42 |
20 |
29 |
72,730 |
2 |
4 |
35 | |
32 |
35 |
40 |
47 |
|
144 |
125 |
90 |
35 |
22 |
300,922 |
2 |
5 |
56 | |
62 |
65 |
77 |
86 |
|
225 |
221 |
156 |
65 |
20 |
958,492 |
2 |
6 |
84 | |
114 |
117 |
138 |
147 |
|
324 |
354 |
240 |
114 |
15 |
2,440,086 |
2 |
7 |
120 | |
195 |
198 |
230 |
237 |
|
441 |
528 |
342 |
186 |
12 |
5,421,379 |
2 |
8 |
165 | |
312 |
315 |
360 |
363 |
|
576 |
747 |
462 |
285 |
9 |
10,727,994 |
2 |
9 |
220 | |
472 |
475 |
535 |
532 |
|
729 |
1011 |
600 |
411 |
8 |
19,962,384 |
2 |
10 |
286 | |
682 |
685 |
762 |
751 |
|
900 |
1320 |
756 |
564 |
6 |
35,069,650 |
2 |
11 |
364 | |
949 |
952 |
1048 |
1027 |
|
1089 |
1674 |
930 |
744 |
5 |
56,408,601 |
2 |
12 |
455 | |
1280 |
1283 |
1400 |
1367 |
|
1296 |
2073 |
1122 |
951 |
5 |
88,479,249 |
2 |
13 |
560 | |
1682 |
1685 |
1825 |
1778 |
|
1521 |
2517 |
1332 |
1185 |
4 |
134,245,309 |
2 |
14 |
680 | |
2162 |
2165 |
2330 |
2267 |
|
1764 |
3006 |
1560 |
1446 |
4 |
195,929,430 |
2 |
15 |
816 | |
2727 |
2730 |
2922 |
2841 |
|
2025 |
3540 |
1806 |
1734 |
3 |
275,441,490 |
2 |
16 |
969 | |
3384 |
3387 |
3608 |
3507 |
|
2304 |
4119 |
2070 |
2049 |
3 |
387,230,647 |
2 |
17 |
1140 | |
4140 |
4143 |
4395 |
4272 |
|
2601 |
4743 |
2352 |
2391 |
3 |
526,031,952 |
2 |
18 |
1330 | |
5002 |
5005 |
5290 |
5143 |
|
2916 |
5412 |
2652 |
2760 |
2 |
705,306,699 |
2 |
19 |
1540 | |
5977 |
5980 |
6300 |
6127 |
|
3249 |
6126 |
2970 |
3156 |
2 |
922,370,359 |
2 |
20 |
1771 | |
7072 |
7075 |
7432 |
7231 |
|
3600 |
6885 |
3306 |
3579 |
2 |
1,225,545,723 |
2 |
21 |
2024 | |
8294 |
8297 |
8693 |
8462 |
|
3969 |
7689 |
3660 |
4029 |
2 |
1,529,677,812 |
2 |
22 |
2300 | |
9650 |
9653 |
10090 |
9827 |
|
4356 |
8538 |
4032 |
4506 |
2 |
1,949,795,527 |
2 |
23 |
2600 | |
11147 |
11150 |
11630 |
11333 |
|
4761 |
9432 |
4422 |
5010 |
2 |
2,444,150,760 |
2 |
24 |
2925 | |
12792 |
12795 |
13320 |
12987 |
|
5184 |
10371 |
4830 |
5541 |
2 |
3,027,647,736 |
2 |
25 |
3276 | |
14592 |
14595 |
15167 |
14796 |
|
5625 |
11355 |
5256 |
6099 |
1 |
3,695,995,057 |
2 |
26 |
3654 | |
16554 |
16557 |
17178 |
16767 |
|
6084 |
12384 |
5700 |
6684 |
1 |
4,513,625,973 |
2 |
27 |
4060 | |
18685 |
18688 |
19360 |
18907 |
|
6561 |
13458 |
6162 |
7296 |
1 |
5,473,913,493 |
2 |
28 |
4495 | |
20992 |
20995 |
21720 |
21223 |
|
7056 |
14577 |
6642 |
7935 |
1 |
6,491,684,515 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
90 |
62 |
42 |
20 |
29 |
82,183 |
3 |
4 |
35 | |
29 |
35 |
35 |
38 |
|
171 |
125 |
90 |
35 |
22 |
420,661 |
3 |
5 |
56 | |
44 |
56 |
59 |
68 |
|
279 |
221 |
165 |
56 |
21 |
1,581,645 |
3 |
6 |
84 | |
72 |
87 |
99 |
114 |
|
414 |
357 |
270 |
87 |
20 |
4,487,345 |
3 |
7 |
120 | |
120 |
138 |
162 |
180 |
|
576 |
540 |
402 |
138 |
17 |
10,403,473 |
3 |
8 |
165 | |
195 |
216 |
255 |
273 |
|
765 |
774 |
561 |
213 |
15 |
21,876,432 |
3 |
9 |
220 | |
304 |
328 |
385 |
400 |
|
981 |
1063 |
747 |
316 |
13 |
41,927,009 |
3 |
10 |
286 | |
454 |
481 |
559 |
568 |
|
1224 |
1411 |
960 |
451 |
11 |
74,205,931 |
3 |
11 |
364 | |
652 |
682 |
784 |
784 |
|
1494 |
1822 |
1200 |
622 |
10 |
125,591,748 |
3 |
12 |
455 | |
905 |
938 |
1067 |
1055 |
|
1791 |
2296 |
1467 |
829 |
9 |
201,434,429 |
3 |
13 |
560 | |
1220 |
1256 |
1415 |
1388 |
|
2115 |
2833 |
1761 |
1072 |
8 |
312,190,126 |
3 |
14 |
680 | |
1604 |
1643 |
1835 |
1790 |
|
2466 |
3433 |
2082 |
1351 |
7 |
457,386,507 |
3 |
15 |
816 | |
2064 |
2106 |
2334 |
2268 |
|
2844 |
4096 |
2430 |
1666 |
6 |
661,849,949 |
3 |
16 |
969 | |
2607 |
2652 |
2919 |
2829 |
|
3249 |
4822 |
2805 |
2017 |
6 |
941,692,516 |
3 |
17 |
1140 | |
3240 |
3288 |
3597 |
3480 |
|
3681 |
5611 |
3207 |
2404 |
5 |
1,303,728,144 |
3 |
18 |
1330 | |
3970 |
4021 |
4375 |
4228 |
|
4140 |
6463 |
3636 |
2827 |
5 |
1,758,568,541 |
3 |
19 |
1540 | |
4804 |
4858 |
5260 |
5080 |
|
4626 |
7378 |
4092 |
3286 |
5 |
2,317,674,853 |
3 |
20 |
1771 | |
5749 |
5806 |
6259 |
6043 |
|
5139 |
8356 |
4575 |
3781 |
4 |
3,007,423,410 |
3 |
21 |
2024 | |
6812 |
6872 |
7379 |
7124 |
|
5679 |
9397 |
5085 |
4312 |
4 |
3,911,619,962 |
3 |
22 |
2300 | |
8000 |
8063 |
8627 |
8330 |
|
6246 |
10501 |
5622 |
4879 |
4 |
4,973,746,369 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
180 |
125 |
90 |
35 |
22 |
472,012 |
4 |
5 |
56 | |
47 |
56 |
56 |
59 |
|
306 |
221 |
165 |
56 |
21 |
1,936,392 |
4 |
6 |
84 | |
63 |
84 |
85 |
96 |
|
468 |
357 |
273 |
84 |
19 |
6,292,201 |
4 |
7 |
120 | |
90 |
120 |
129 |
150 |
|
666 |
540 |
420 |
120 |
18 |
17,061,911 |
4 |
8 |
165 | |
135 |
171 |
195 |
225 |
|
900 |
777 |
606 |
171 |
17 |
36,630,982 |
4 |
9 |
220 | |
205 |
247 |
290 |
325 |
|
1170 |
1075 |
828 |
247 |
16 |
75,701,459 |
4 |
10 |
286 | |
307 |
355 |
421 |
457 |
|
1476 |
1438 |
1086 |
352 |
15 |
138,961,265 |
4 |
11 |
364 | |
448 |
502 |
595 |
628 |
|
1818 |
1870 |
1380 |
490 |
14 |
238,702,094 |
4 |
12 |
455 | |
635 |
695 |
819 |
845 |
|
2196 |
2375 |
1710 |
665 |
13 |
399,624,449 |
4 |
13 |
560 | |
875 |
941 |
1100 |
1115 |
|
2610 |
2957 |
2076 |
881 |
12 |
627,247,617 |
4 |
14 |
680 | |
1175 |
1247 |
1445 |
1445 |
|
3060 |
3620 |
2478 |
1142 |
11 |
935,438,934 |
4 |
15 |
816 | |
1542 |
1620 |
1861 |
1842 |
|
3546 |
4364 |
2916 |
1448 |
10 |
1,364,526,664 |
4 |
16 |
969 | |
1983 |
2067 |
2355 |
2313 |
|
4068 |
5189 |
3390 |
1799 |
9 |
1,977,307,046 |
4 |
17 |
1140 | |
2505 |
2595 |
2934 |
2865 |
|
4626 |
6095 |
3900 |
2195 |
8 |
2,744,781,287 |
4 |
18 |
1330 | |
3115 |
3211 |
3605 |
3505 |
|
5220 |
7082 |
4446 |
2636 |
8 |
3,750,315,135 |
4 |
19 |
1540 | |
3820 |
3922 |
4375 |
4240 |
|
5850 |
8150 |
5028 |
3122 |
7 |
4,972,137,886 |
4 |
20 |
1771 | |
4627 |
4735 |
5251 |
5077 |
|
6516 |
9299 |
5646 |
3653 |
7 |
6,563,569,792 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
315 |
221 |
165 |
56 |
21 |
2,167,332 |
5 |
6 |
84 | |
72 |
84 |
84 |
87 |
|
495 |
357 |
273 |
84 |
19 |
7,337,437 |
5 |
7 |
120 | |
90 |
120 |
121 |
132 |
|
720 |
540 |
420 |
120 |
18 |
20,416,610 |
5 |
8 |
165 | |
117 |
165 |
172 |
195 |
|
990 |
777 |
612 |
165 |
16 |
50,735,136 |
5 |
9 |
220 | |
160 |
220 |
244 |
280 |
|
1305 |
1075 |
855 |
220 |
14 |
109,579,803 |
5 |
10 |
286 | |
226 |
295 |
344 |
391 |
|
1665 |
1441 |
1146 |
295 |
13 |
213,848,068 |
5 |
11 |
364 | |
322 |
400 |
479 |
532 |
|
2070 |
1882 |
1482 |
400 |
12 |
381,816,570 |
5 |
12 |
455 | |
455 |
542 |
656 |
710 |
|
2520 |
2402 |
1863 |
539 |
11 |
631,213,247 |
5 |
13 |
560 | |
632 |
728 |
882 |
932 |
|
3015 |
3005 |
2289 |
716 |
10 |
998,814,863 |
5 |
14 |
680 | |
860 |
965 |
1164 |
1205 |
|
3555 |
3695 |
2760 |
935 |
9 |
1,547,386,388 |
5 |
15 |
816 | |
1146 |
1260 |
1509 |
1536 |
|
4140 |
4476 |
3276 |
1200 |
8 |
2,252,365,712 |
5 |
16 |
969 | |
1497 |
1620 |
1924 |
1932 |
|
4770 |
5352 |
3837 |
1515 |
7 |
3,283,959,465 |
5 |
17 |
1140 | |
1920 |
2052 |
2416 |
2400 |
|
5445 |
6327 |
4443 |
1884 |
7 |
4,593,569,277 |
5 |
18 |
1330 | |
2422 |
2563 |
2992 |
2947 |
|
6165 |
7401 |
5094 |
2307 |
6 |
6,316,570,748 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
504 |
357 |
273 |
84 |
19 |
7,711,684 |
6 |
7 |
120 | |
105 |
120 |
120 |
123 |
|
747 |
540 |
420 |
120 |
18 |
22,867,472 |
6 |
8 |
165 | |
126 |
165 |
166 |
177 |
|
1044 |
777 |
612 |
165 |
16 |
57,160,011 |
6 |
9 |
220 | |
154 |
220 |
225 |
250 |
|
1395 |
1075 |
855 |
220 |
14 |
130,657,506 |
6 |
10 |
286 | |
196 |
286 |
304 |
346 |
|
1800 |
1441 |
1155 |
286 |
13 |
268,624,798 |
6 |
11 |
364 | |
259 |
364 |
410 |
469 |
|
2259 |
1882 |
1518 |
364 |
12 |
503,842,107 |
6 |
12 |
455 | |
350 |
470 |
550 |
623 |
|
2772 |
2405 |
1935 |
470 |
12 |
857,621,956 |
6 |
13 |
560 | |
476 |
611 |
731 |
812 |
|
3339 |
3017 |
2406 |
611 |
12 |
1,444,505,531 |
6 |
14 |
680 | |
644 |
794 |
960 |
1043 |
|
3960 |
3722 |
2931 |
791 |
11 |
2,229,532,616 |
6 |
15 |
816 | |
861 |
1026 |
1244 |
1323 |
|
4635 |
4524 |
3510 |
1014 |
11 |
3,393,306,561 |
6 |
16 |
969 | |
1134 |
1314 |
1590 |
1659 |
|
5364 |
5427 |
4143 |
1284 |
10 |
4,982,135,270 |
6 |
17 |
1140 | |
1470 |
1665 |
2005 |
2058 |
|
6147 |
6435 |
4830 |
1605 |
9 |
7,012,816,784 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
756 |
540 |
420 |
120 |
18 |
23,718,719 |
7 |
8 |
165 | |
147 |
165 |
165 |
168 |
|
1071 |
777 |
612 |
165 |
16 |
60,749,907 |
7 |
9 |
220 | |
172 |
220 |
221 |
232 |
|
1449 |
1075 |
855 |
220 |
14 |
141,293,262 |
7 |
10 |
286 | |
202 |
286 |
290 |
316 |
|
1890 |
1441 |
1155 |
286 |
13 |
293,539,924 |
7 |
11 |
364 | |
244 |
364 |
378 |
424 |
|
2394 |
1882 |
1518 |
364 |
12 |
580,169,253 |
7 |
12 |
455 | |
305 |
455 |
492 |
560 |
|
2961 |
2405 |
1950 |
455 |
12 |
1,047,441,337 |
7 |
13 |
560 | |
392 |
563 |
639 |
728 |
|
3591 |
3017 |
2454 |
563 |
11 |
1,799,225,713 |
7 |
14 |
680 | |
512 |
704 |
826 |
932 |
|
4284 |
3725 |
3021 |
704 |
11 |
2,875,565,424 |
7 |
15 |
816 | |
672 |
885 |
1060 |
1176 |
|
5040 |
4536 |
3651 |
885 |
10 |
4,428,401,166 |
7 |
16 |
969 | |
879 |
1113 |
1348 |
1467 |
|
5859 |
5454 |
4344 |
1110 |
10 |
6,574,135,753 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
1080 |
777 |
612 |
165 |
16 |
61,428,363 |
8 |
9 |
220 | |
199 |
220 |
220 |
223 |
|
1476 |
1075 |
855 |
220 |
14 |
148,257,483 |
8 |
10 |
286 | |
229 |
286 |
287 |
298 |
|
1944 |
1441 |
1155 |
286 |
13 |
318,273,733 |
8 |
11 |
364 | |
262 |
364 |
368 |
394 |
|
2484 |
1882 |
1518 |
364 |
12 |
630,119,607 |
8 |
12 |
455 | |
305 |
455 |
467 |
515 |
|
3096 |
2405 |
1950 |
455 |
12 |
1,149,180,871 |
8 |
13 |
560 | |
365 |
560 |
591 |
665 |
|
3780 |
3017 |
2457 |
560 |
11 |
2,002,946,913 |
8 |
14 |
680 | |
449 |
680 |
747 |
848 |
|
4536 |
3725 |
3045 |
680 |
10 |
3,388,146,512 |
8 |
15 |
816 | |
564 |
822 |
942 |
1068 |
|
5364 |
4536 |
3714 |
822 |
10 |
5,366,736,041 |
8 |
16 |
969 | |
717 |
1002 |
1183 |
1329 |
|
6264 |
5457 |
4455 |
1002 |
10 |
8,161,892,805 |
|
Bounds and Dimensions on generic MS cone
shelling parameters: a0 = 1 a1 = 3 a2 = 3 a3 = 0
Combinatorics:
7 | tetrahedra |
9 | interior faces |
3 | interior edges |
0 | interior vertices |
| |
10 | boundary faces |
15 | boundary edges |
7 | boundary vertices |
| |
19 | faces total |
18 | edges total |
7 | vertices total |