Bounds and Dimensions on symmetric 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 |
11 |
11 |
13 |
|
27 |
25 |
14 |
11 |
32 |
8,537 |
1 |
3 |
20 | |
26 |
27 |
29 |
32 |
|
54 |
62 |
35 |
27 |
21 |
29,360 |
1 |
4 |
35 | |
59 |
60 |
65 |
68 |
|
90 |
122 |
65 |
57 |
12 |
86,780 |
1 |
5 |
56 | |
116 |
117 |
126 |
128 |
|
135 |
209 |
104 |
105 |
11 |
199,481 |
1 |
6 |
84 | |
204 |
205 |
219 |
219 |
|
189 |
323 |
152 |
171 |
7 |
441,128 |
1 |
7 |
120 | |
330 |
331 |
351 |
348 |
|
252 |
464 |
209 |
255 |
7 |
789,605 |
1 |
8 |
165 | |
501 |
502 |
529 |
522 |
|
324 |
632 |
275 |
357 |
5 |
1,405,389 |
1 |
9 |
220 | |
724 |
725 |
760 |
748 |
|
405 |
827 |
350 |
477 |
5 |
2,188,827 |
1 |
10 |
286 | |
1006 |
1007 |
1051 |
1033 |
|
495 |
1049 |
434 |
615 |
3 |
3,611,510 |
1 |
11 |
364 | |
1354 |
1355 |
1409 |
1384 |
|
594 |
1298 |
527 |
771 |
3 |
5,119,928 |
1 |
12 |
455 | |
1775 |
1776 |
1841 |
1808 |
|
702 |
1574 |
629 |
945 |
3 |
7,653,194 |
1 |
13 |
560 | |
2276 |
2277 |
2354 |
2312 |
|
819 |
1877 |
740 |
1137 |
3 |
10,291,535 |
1 |
14 |
680 | |
2864 |
2865 |
2955 |
2903 |
|
945 |
2207 |
860 |
1347 |
2 |
14,033,106 |
1 |
15 |
816 | |
3546 |
3547 |
3651 |
3588 |
|
1080 |
2564 |
989 |
1575 |
2 |
18,668,901 |
1 |
16 |
969 | |
4329 |
4330 |
4449 |
4374 |
|
1224 |
2948 |
1127 |
1821 |
2 |
24,449,132 |
1 |
17 |
1140 | |
5220 |
5221 |
5356 |
5268 |
|
1377 |
3359 |
1274 |
2085 |
2 |
31,087,943 |
1 |
18 |
1330 | |
6226 |
6227 |
6379 |
6277 |
|
1539 |
3797 |
1430 |
2367 |
2 |
39,144,878 |
1 |
19 |
1540 | |
7354 |
7355 |
7525 |
7408 |
|
1710 |
4262 |
1595 |
2667 |
2 |
48,435,830 |
1 |
20 |
1771 | |
8611 |
8612 |
8801 |
8668 |
|
1890 |
4754 |
1769 |
2985 |
1 |
60,386,073 |
1 |
21 |
2024 | |
10004 |
10005 |
10214 |
10064 |
|
2079 |
5273 |
1952 |
3321 |
1 |
72,269,145 |
1 |
22 |
2300 | |
11540 |
11541 |
11771 |
11603 |
|
2277 |
5819 |
2144 |
3675 |
1 |
90,922,964 |
1 |
23 |
2600 | |
13226 |
13227 |
13479 |
13292 |
|
2484 |
6392 |
2345 |
4047 |
1 |
103,883,321 |
1 |
24 |
2925 | |
15069 |
15070 |
15345 |
15138 |
|
2700 |
6992 |
2555 |
4437 |
1 |
124,893,089 |
1 |
25 |
3276 | |
17076 |
17077 |
17376 |
17148 |
|
2925 |
7619 |
2774 |
4845 |
1 |
145,161,185 |
1 |
26 |
3654 | |
19254 |
19255 |
19579 |
19329 |
|
3159 |
8273 |
3002 |
5271 |
1 |
173,226,669 |
1 |
27 |
4060 | |
21610 |
21611 |
21961 |
21688 |
|
3402 |
8954 |
3239 |
5715 |
1 |
200,265,783 |
1 |
28 |
4495 | |
24151 |
24152 |
24529 |
24232 |
|
3654 |
9662 |
3485 |
6177 |
1 |
237,562,133 |
1 |
29 |
4960 | |
26884 |
26885 |
27290 |
26968 |
|
3915 |
10397 |
3740 |
6657 |
1 |
265,452,302 |
1 |
30 |
5456 | |
29816 |
29817 |
30251 |
29903 |
|
4185 |
11159 |
4004 |
7155 |
1 |
307,323,905 |
1 |
31 |
5984 | |
32954 |
32955 |
33419 |
33044 |
|
4464 |
11948 |
4277 |
7671 |
1 |
351,517,289 |
1 |
32 |
6545 | |
36305 |
36306 |
36801 |
36398 |
|
4752 |
12764 |
4559 |
8205 |
1 |
400,812,144 |
1 |
33 |
7140 | |
39876 |
39877 |
40404 |
39972 |
|
5049 |
13607 |
4850 |
8757 |
1 |
450,149,457 |
1 |
34 |
7770 | |
43674 |
43675 |
44235 |
43773 |
|
5355 |
14477 |
5150 |
9327 |
1 |
511,791,839 |
1 |
35 |
8436 | |
47706 |
47707 |
48301 |
47808 |
|
5670 |
15374 |
5459 |
9915 |
1 |
565,733,912 |
1 |
36 |
9139 | |
51979 |
51980 |
52609 |
52084 |
|
5994 |
16298 |
5777 |
10521 |
1 |
640,313,048 |
1 |
37 |
9880 | |
56500 |
56501 |
57166 |
56608 |
|
6327 |
17249 |
6104 |
11145 |
1 |
712,507,238 |
1 |
38 |
10660 | |
61276 |
61277 |
61979 |
61387 |
|
6669 |
18227 |
6440 |
11787 |
0 |
806,581,158 |
1 |
39 |
11480 | |
66314 |
66315 |
67055 |
66428 |
|
7020 |
19232 |
6785 |
12447 |
0 |
876,830,118 |
1 |
40 |
12341 | |
71621 |
71622 |
72401 |
71738 |
|
7380 |
20264 |
7139 |
13125 |
0 |
977,492,270 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
36 |
25 |
15 |
10 |
40 |
8,274 |
2 |
3 |
20 | |
17 |
20 |
20 |
23 |
|
81 |
62 |
42 |
20 |
29 |
72,442 |
2 |
4 |
35 | |
32 |
36 |
40 |
47 |
|
144 |
125 |
89 |
36 |
23 |
296,063 |
2 |
5 |
56 | |
62 |
66 |
77 |
86 |
|
225 |
221 |
155 |
66 |
19 |
941,318 |
2 |
6 |
84 | |
114 |
118 |
138 |
147 |
|
324 |
354 |
239 |
115 |
15 |
2,395,259 |
2 |
7 |
120 | |
195 |
199 |
230 |
237 |
|
441 |
528 |
341 |
187 |
11 |
5,343,731 |
2 |
8 |
165 | |
312 |
316 |
360 |
363 |
|
576 |
747 |
461 |
286 |
9 |
10,555,442 |
2 |
9 |
220 | |
472 |
476 |
535 |
532 |
|
729 |
1011 |
599 |
412 |
7 |
19,678,546 |
2 |
10 |
286 | |
682 |
686 |
762 |
751 |
|
900 |
1320 |
755 |
565 |
6 |
34,607,472 |
2 |
11 |
364 | |
949 |
953 |
1048 |
1027 |
|
1089 |
1674 |
929 |
745 |
5 |
55,759,645 |
2 |
12 |
455 | |
1280 |
1284 |
1400 |
1367 |
|
1296 |
2073 |
1121 |
952 |
5 |
87,353,805 |
2 |
13 |
560 | |
1682 |
1686 |
1825 |
1778 |
|
1521 |
2517 |
1331 |
1186 |
4 |
133,026,700 |
2 |
14 |
680 | |
2162 |
2166 |
2330 |
2267 |
|
1764 |
3006 |
1559 |
1447 |
4 |
194,263,485 |
2 |
15 |
816 | |
2727 |
2731 |
2922 |
2841 |
|
2025 |
3540 |
1805 |
1735 |
3 |
273,274,152 |
2 |
16 |
969 | |
3384 |
3388 |
3608 |
3507 |
|
2304 |
4119 |
2069 |
2050 |
3 |
383,095,220 |
2 |
17 |
1140 | |
4140 |
4144 |
4395 |
4272 |
|
2601 |
4743 |
2351 |
2392 |
3 |
521,528,721 |
2 |
18 |
1330 | |
5002 |
5006 |
5290 |
5143 |
|
2916 |
5412 |
2651 |
2761 |
2 |
698,735,565 |
2 |
19 |
1540 | |
5977 |
5981 |
6300 |
6127 |
|
3249 |
6126 |
2969 |
3157 |
2 |
916,395,456 |
2 |
20 |
1771 | |
7072 |
7076 |
7432 |
7231 |
|
3600 |
6885 |
3305 |
3580 |
2 |
1,215,312,309 |
2 |
21 |
2024 | |
8294 |
8298 |
8693 |
8462 |
|
3969 |
7689 |
3659 |
4030 |
2 |
1,517,924,273 |
2 |
22 |
2300 | |
9650 |
9654 |
10090 |
9827 |
|
4356 |
8538 |
4031 |
4507 |
2 |
1,928,813,723 |
2 |
23 |
2600 | |
11147 |
11151 |
11630 |
11333 |
|
4761 |
9432 |
4421 |
5011 |
2 |
2,424,274,806 |
2 |
24 |
2925 | |
12792 |
12796 |
13320 |
12987 |
|
5184 |
10371 |
4829 |
5542 |
2 |
3,004,216,683 |
2 |
25 |
3276 | |
14592 |
14596 |
15167 |
14796 |
|
5625 |
11355 |
5255 |
6100 |
1 |
3,654,863,443 |
2 |
26 |
3654 | |
16554 |
16558 |
17178 |
16767 |
|
6084 |
12384 |
5699 |
6685 |
1 |
4,478,597,754 |
2 |
27 |
4060 | |
18685 |
18689 |
19360 |
18907 |
|
6561 |
13458 |
6161 |
7297 |
1 |
5,429,635,975 |
2 |
28 |
4495 | |
20992 |
20996 |
21720 |
21223 |
|
7056 |
14577 |
6641 |
7936 |
1 |
6,447,144,881 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
90 |
62 |
42 |
20 |
29 |
81,757 |
3 |
4 |
35 | |
29 |
35 |
35 |
38 |
|
171 |
125 |
90 |
35 |
22 |
416,908 |
3 |
5 |
56 | |
44 |
56 |
59 |
68 |
|
279 |
221 |
165 |
56 |
20 |
1,562,017 |
3 |
6 |
84 | |
72 |
88 |
99 |
114 |
|
414 |
357 |
269 |
88 |
19 |
4,431,052 |
3 |
7 |
120 | |
120 |
139 |
162 |
180 |
|
576 |
540 |
401 |
139 |
18 |
10,305,528 |
3 |
8 |
165 | |
195 |
217 |
255 |
273 |
|
765 |
774 |
560 |
214 |
16 |
21,743,924 |
3 |
9 |
220 | |
304 |
329 |
385 |
400 |
|
981 |
1063 |
746 |
317 |
14 |
41,770,203 |
3 |
10 |
286 | |
454 |
482 |
559 |
568 |
|
1224 |
1411 |
959 |
452 |
13 |
73,935,833 |
3 |
11 |
364 | |
652 |
683 |
784 |
784 |
|
1494 |
1822 |
1199 |
623 |
12 |
125,262,914 |
3 |
12 |
455 | |
905 |
939 |
1067 |
1055 |
|
1791 |
2296 |
1466 |
830 |
10 |
201,408,037 |
3 |
13 |
560 | |
1220 |
1257 |
1415 |
1388 |
|
2115 |
2833 |
1760 |
1073 |
9 |
312,304,359 |
3 |
14 |
680 | |
1604 |
1644 |
1835 |
1790 |
|
2466 |
3433 |
2081 |
1352 |
9 |
458,069,973 |
3 |
15 |
816 | |
2064 |
2107 |
2334 |
2268 |
|
2844 |
4096 |
2429 |
1667 |
8 |
663,777,392 |
3 |
16 |
969 | |
2607 |
2653 |
2919 |
2829 |
|
3249 |
4822 |
2804 |
2018 |
7 |
943,405,307 |
3 |
17 |
1140 | |
3240 |
3289 |
3597 |
3480 |
|
3681 |
5611 |
3206 |
2405 |
7 |
1,304,282,354 |
3 |
18 |
1330 | |
3970 |
4022 |
4375 |
4228 |
|
4140 |
6463 |
3635 |
2828 |
6 |
1,762,901,279 |
3 |
19 |
1540 | |
4804 |
4859 |
5260 |
5080 |
|
4626 |
7378 |
4091 |
3287 |
6 |
2,322,332,401 |
3 |
20 |
1771 | |
5749 |
5807 |
6259 |
6043 |
|
5139 |
8356 |
4574 |
3782 |
6 |
3,011,355,487 |
3 |
21 |
2024 | |
6812 |
6873 |
7379 |
7124 |
|
5679 |
9397 |
5084 |
4313 |
5 |
3,922,255,701 |
3 |
22 |
2300 | |
8000 |
8064 |
8627 |
8330 |
|
6246 |
10501 |
5621 |
4880 |
5 |
4,985,425,337 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
180 |
125 |
90 |
35 |
22 |
469,168 |
4 |
5 |
56 | |
47 |
56 |
56 |
59 |
|
306 |
221 |
165 |
56 |
20 |
1,922,512 |
4 |
6 |
84 | |
63 |
84 |
85 |
96 |
|
468 |
357 |
273 |
84 |
18 |
6,254,486 |
4 |
7 |
120 | |
90 |
121 |
129 |
150 |
|
666 |
540 |
419 |
121 |
18 |
16,943,244 |
4 |
8 |
165 | |
135 |
173 |
195 |
225 |
|
900 |
777 |
604 |
173 |
17 |
36,311,516 |
4 |
9 |
220 | |
205 |
249 |
290 |
325 |
|
1170 |
1075 |
826 |
249 |
16 |
75,393,704 |
4 |
10 |
286 | |
307 |
357 |
421 |
457 |
|
1476 |
1438 |
1084 |
354 |
15 |
138,915,153 |
4 |
11 |
364 | |
448 |
504 |
595 |
628 |
|
1818 |
1870 |
1378 |
492 |
14 |
237,281,260 |
4 |
12 |
455 | |
635 |
697 |
819 |
845 |
|
2196 |
2375 |
1708 |
667 |
13 |
397,633,013 |
4 |
13 |
560 | |
875 |
943 |
1100 |
1115 |
|
2610 |
2957 |
2074 |
883 |
12 |
625,174,242 |
4 |
14 |
680 | |
1175 |
1249 |
1445 |
1445 |
|
3060 |
3620 |
2476 |
1144 |
11 |
939,168,117 |
4 |
15 |
816 | |
1542 |
1622 |
1861 |
1842 |
|
3546 |
4364 |
2914 |
1450 |
10 |
1,359,852,876 |
4 |
16 |
969 | |
1983 |
2069 |
2355 |
2313 |
|
4068 |
5189 |
3388 |
1801 |
9 |
1,970,689,088 |
4 |
17 |
1140 | |
2505 |
2597 |
2934 |
2865 |
|
4626 |
6095 |
3898 |
2197 |
8 |
2,744,989,038 |
4 |
18 |
1330 | |
3115 |
3213 |
3605 |
3505 |
|
5220 |
7082 |
4444 |
2638 |
8 |
3,744,345,434 |
4 |
19 |
1540 | |
3820 |
3924 |
4375 |
4240 |
|
5850 |
8150 |
5026 |
3124 |
7 |
4,947,862,095 |
4 |
20 |
1771 | |
4627 |
4737 |
5251 |
5077 |
|
6516 |
9299 |
5644 |
3655 |
7 |
6,551,136,594 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
315 |
221 |
165 |
56 |
20 |
2,155,309 |
5 |
6 |
84 | |
72 |
84 |
84 |
87 |
|
495 |
357 |
273 |
84 |
18 |
7,299,977 |
5 |
7 |
120 | |
90 |
120 |
121 |
132 |
|
720 |
540 |
420 |
120 |
17 |
20,297,592 |
5 |
8 |
165 | |
117 |
165 |
172 |
195 |
|
990 |
777 |
612 |
165 |
16 |
50,701,435 |
5 |
9 |
220 | |
160 |
221 |
244 |
280 |
|
1305 |
1075 |
854 |
221 |
14 |
109,239,082 |
5 |
10 |
286 | |
226 |
297 |
344 |
391 |
|
1665 |
1441 |
1144 |
297 |
13 |
213,233,201 |
5 |
11 |
364 | |
322 |
402 |
479 |
532 |
|
2070 |
1882 |
1480 |
402 |
12 |
379,952,675 |
5 |
12 |
455 | |
455 |
544 |
656 |
710 |
|
2520 |
2402 |
1861 |
541 |
12 |
628,910,006 |
5 |
13 |
560 | |
632 |
730 |
882 |
932 |
|
3015 |
3005 |
2287 |
718 |
11 |
996,320,959 |
5 |
14 |
680 | |
860 |
967 |
1164 |
1205 |
|
3555 |
3695 |
2758 |
937 |
10 |
1,543,238,991 |
5 |
15 |
816 | |
1146 |
1262 |
1509 |
1536 |
|
4140 |
4476 |
3274 |
1202 |
9 |
2,246,475,736 |
5 |
16 |
969 | |
1497 |
1622 |
1924 |
1932 |
|
4770 |
5352 |
3835 |
1517 |
8 |
3,276,001,549 |
5 |
17 |
1140 | |
1920 |
2054 |
2416 |
2400 |
|
5445 |
6327 |
4441 |
1886 |
8 |
4,583,422,617 |
5 |
18 |
1330 | |
2422 |
2565 |
2992 |
2947 |
|
6165 |
7401 |
5092 |
2309 |
7 |
6,302,997,073 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
504 |
357 |
273 |
84 |
18 |
7,646,984 |
6 |
7 |
120 | |
105 |
120 |
120 |
123 |
|
747 |
540 |
420 |
120 |
17 |
22,721,826 |
6 |
8 |
165 | |
126 |
165 |
166 |
177 |
|
1044 |
777 |
612 |
165 |
16 |
57,028,507 |
6 |
9 |
220 | |
154 |
220 |
225 |
250 |
|
1395 |
1075 |
855 |
220 |
14 |
130,171,909 |
6 |
10 |
286 | |
196 |
286 |
304 |
346 |
|
1800 |
1441 |
1155 |
286 |
13 |
268,192,171 |
6 |
11 |
364 | |
259 |
368 |
410 |
469 |
|
2259 |
1882 |
1514 |
368 |
12 |
501,693,071 |
6 |
12 |
455 | |
350 |
475 |
550 |
623 |
|
2772 |
2405 |
1930 |
475 |
12 |
854,406,956 |
6 |
13 |
560 | |
476 |
616 |
731 |
812 |
|
3339 |
3017 |
2401 |
616 |
12 |
1,439,157,025 |
6 |
14 |
680 | |
644 |
799 |
960 |
1043 |
|
3960 |
3722 |
2926 |
796 |
11 |
2,223,074,013 |
6 |
15 |
816 | |
861 |
1031 |
1244 |
1323 |
|
4635 |
4524 |
3505 |
1019 |
11 |
3,390,548,805 |
6 |
16 |
969 | |
1134 |
1319 |
1590 |
1659 |
|
5364 |
5427 |
4138 |
1289 |
10 |
4,975,274,372 |
6 |
17 |
1140 | |
1470 |
1670 |
2005 |
2058 |
|
6147 |
6435 |
4825 |
1610 |
9 |
7,006,139,939 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
756 |
540 |
420 |
120 |
17 |
23,564,442 |
7 |
8 |
165 | |
147 |
165 |
165 |
168 |
|
1071 |
777 |
612 |
165 |
16 |
60,509,224 |
7 |
9 |
220 | |
172 |
220 |
221 |
232 |
|
1449 |
1075 |
855 |
220 |
14 |
140,720,623 |
7 |
10 |
286 | |
202 |
286 |
290 |
316 |
|
1890 |
1441 |
1155 |
286 |
13 |
292,731,550 |
7 |
11 |
364 | |
244 |
364 |
378 |
424 |
|
2394 |
1882 |
1518 |
364 |
12 |
578,653,783 |
7 |
12 |
455 | |
305 |
456 |
492 |
560 |
|
2961 |
2405 |
1949 |
456 |
12 |
1,044,971,319 |
7 |
13 |
560 | |
392 |
568 |
639 |
728 |
|
3591 |
3017 |
2449 |
568 |
11 |
1,792,782,061 |
7 |
14 |
680 | |
512 |
710 |
826 |
932 |
|
4284 |
3725 |
3015 |
710 |
11 |
2,867,169,494 |
7 |
15 |
816 | |
672 |
891 |
1060 |
1176 |
|
5040 |
4536 |
3645 |
891 |
10 |
4,417,411,673 |
7 |
16 |
969 | |
879 |
1119 |
1348 |
1467 |
|
5859 |
5454 |
4338 |
1116 |
10 |
6,558,290,916 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
1080 |
777 |
612 |
165 |
16 |
60,893,692 |
8 |
9 |
220 | |
199 |
220 |
220 |
223 |
|
1476 |
1075 |
855 |
220 |
14 |
147,379,030 |
8 |
10 |
286 | |
229 |
286 |
287 |
298 |
|
1944 |
1441 |
1155 |
286 |
13 |
317,228,977 |
8 |
11 |
364 | |
262 |
364 |
368 |
394 |
|
2484 |
1882 |
1518 |
364 |
12 |
627,938,644 |
8 |
12 |
455 | |
305 |
455 |
467 |
515 |
|
3096 |
2405 |
1950 |
455 |
12 |
1,146,288,675 |
8 |
13 |
560 | |
365 |
560 |
591 |
665 |
|
3780 |
3017 |
2457 |
560 |
11 |
1,999,310,559 |
8 |
14 |
680 | |
449 |
681 |
747 |
848 |
|
4536 |
3725 |
3044 |
681 |
10 |
3,378,983,326 |
8 |
15 |
816 | |
564 |
827 |
942 |
1068 |
|
5364 |
4536 |
3709 |
827 |
10 |
5,347,396,113 |
8 |
16 |
969 | |
717 |
1008 |
1183 |
1329 |
|
6264 |
5457 |
4449 |
1008 |
10 |
8,143,575,436 |
|
Bounds and Dimensions on symmetric 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 |