Bounds and Dimensions on the regular type-IV 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 |
|
36 |
15 |
11 |
4 |
72 |
5,231 |
1 |
2 |
10 | |
10 |
16 |
18 |
21 |
|
108 |
65 |
49 |
16 |
26 |
102,640 |
1 |
3 |
20 | |
40 |
52 |
60 |
64 |
|
216 |
175 |
123 |
52 |
13 |
457,570 |
1 |
4 |
35 | |
118 |
136 |
154 |
156 |
|
360 |
369 |
233 |
136 |
7 |
1,676,222 |
1 |
5 |
56 | |
268 |
292 |
324 |
320 |
|
540 |
671 |
379 |
292 |
4 |
5,063,372 |
1 |
6 |
84 | |
514 |
544 |
594 |
580 |
|
756 |
1081 |
561 |
520 |
3 |
12,863,361 |
1 |
7 |
120 | |
880 |
916 |
988 |
960 |
|
1008 |
1599 |
779 |
820 |
2 |
28,355,129 |
1 |
8 |
165 | |
1390 |
1432 |
1530 |
1484 |
|
1296 |
2225 |
1033 |
1192 |
2 |
56,660,388 |
1 |
9 |
220 | |
2068 |
2116 |
2244 |
2176 |
|
1620 |
2959 |
1323 |
1636 |
2 |
103,754,666 |
1 |
10 |
286 | |
2938 |
2992 |
3154 |
3060 |
|
1980 |
3801 |
1649 |
2152 |
1 |
179,891,426 |
1 |
11 |
364 | |
4024 |
4084 |
4284 |
4160 |
|
2376 |
4751 |
2011 |
2740 |
1 |
293,160,592 |
1 |
12 |
455 | |
5350 |
5416 |
5658 |
5500 |
|
2808 |
5809 |
2409 |
3400 |
1 |
456,350,233 |
1 |
13 |
560 | |
6940 |
7012 |
7300 |
7104 |
|
3276 |
6975 |
2843 |
4132 |
1 |
688,507,454 |
1 |
14 |
680 | |
8818 |
8896 |
9234 |
8996 |
|
3780 |
8249 |
3313 |
4936 |
1 |
1,008,660,182 |
1 |
15 |
816 | |
11008 |
11092 |
11484 |
11200 |
|
4320 |
9631 |
3819 |
5812 |
1 |
1,435,504,413 |
1 |
16 |
969 | |
13534 |
13624 |
14074 |
13740 |
|
4896 |
11121 |
4361 |
6760 |
1 |
2,000,366,192 |
1 |
17 |
1140 | |
16420 |
16516 |
17028 |
16640 |
|
5508 |
12719 |
4939 |
7780 |
1 |
2,725,776,759 |
1 |
18 |
1330 | |
19690 |
19792 |
20370 |
19924 |
|
6156 |
14425 |
5553 |
8872 |
1 |
3,655,000,550 |
1 |
19 |
1540 | |
23368 |
23476 |
24124 |
23616 |
|
6840 |
16239 |
6203 |
10036 |
1 |
4,838,615,315 |
1 |
20 |
1771 | |
27478 |
27592 |
28314 |
27740 |
|
7560 |
18161 |
6889 |
11272 |
1 |
6,265,659,910 |
1 |
21 |
2024 | |
32044 |
32164 |
32964 |
32320 |
|
8316 |
20191 |
7611 |
12580 |
1 |
8,026,796,884 |
1 |
22 |
2300 | |
37090 |
37216 |
38098 |
37380 |
|
9108 |
22329 |
8369 |
13960 |
1 |
10,178,843,915 |
1 |
23 |
2600 | |
42640 |
42772 |
43740 |
42944 |
|
9936 |
24575 |
9163 |
15412 |
1 |
12,759,719,294 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
144 |
65 |
55 |
10 |
58 |
191,739 |
2 |
3 |
20 | |
9 |
26 |
28 |
31 |
|
324 |
175 |
149 |
26 |
44 |
1,507,423 |
2 |
4 |
35 | |
21 |
63 |
70 |
79 |
|
576 |
369 |
306 |
63 |
23 |
6,977,330 |
2 |
5 |
56 | |
69 |
137 |
154 |
166 |
|
900 |
671 |
534 |
137 |
18 |
21,459,802 |
2 |
6 |
84 | |
177 |
271 |
304 |
315 |
|
1296 |
1105 |
834 |
271 |
13 |
60,814,160 |
2 |
7 |
120 | |
369 |
489 |
544 |
549 |
|
1764 |
1695 |
1206 |
489 |
9 |
140,838,224 |
2 |
8 |
165 | |
669 |
815 |
898 |
891 |
|
2304 |
2465 |
1650 |
815 |
6 |
313,958,381 |
2 |
9 |
220 | |
1101 |
1273 |
1390 |
1365 |
|
2916 |
3415 |
2166 |
1249 |
5 |
619,296,703 |
2 |
10 |
286 | |
1689 |
1887 |
2044 |
1995 |
|
3600 |
4545 |
2754 |
1791 |
4 |
1,025,259,342 |
2 |
11 |
364 | |
2457 |
2681 |
2884 |
2805 |
|
4356 |
5855 |
3414 |
2441 |
3 |
2,082,876,422 |
2 |
12 |
455 | |
3429 |
3679 |
3934 |
3819 |
|
5184 |
7345 |
4146 |
3199 |
3 |
3,278,189,637 |
2 |
13 |
560 | |
4629 |
4905 |
5218 |
5061 |
|
6084 |
9015 |
4950 |
4065 |
2 |
5,378,240,470 |
2 |
14 |
680 | |
6081 |
6383 |
6760 |
6555 |
|
7056 |
10865 |
5826 |
5039 |
2 |
8,390,889,492 |
2 |
15 |
816 | |
7809 |
8137 |
8584 |
8325 |
|
8100 |
12895 |
6774 |
6121 |
2 |
12,308,485,094 |
2 |
16 |
969 | |
9837 |
10191 |
10714 |
10395 |
|
9216 |
15105 |
7794 |
7311 |
2 |
18,255,839,377 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
360 |
175 |
155 |
20 |
66 |
2,189,819 |
3 |
4 |
35 | |
13 |
41 |
43 |
46 |
|
684 |
369 |
328 |
41 |
49 |
13,926,365 |
3 |
5 |
56 | |
9 |
80 |
88 |
100 |
|
1116 |
671 |
591 |
80 |
46 |
66,743,725 |
3 |
6 |
84 | |
29 |
152 |
171 |
194 |
|
1656 |
1105 |
953 |
152 |
43 |
225,632,997 |
3 |
7 |
120 | |
97 |
272 |
310 |
340 |
|
2304 |
1695 |
1423 |
272 |
31 |
541,206,466 |
3 |
8 |
165 | |
237 |
464 |
529 |
561 |
|
3060 |
2465 |
2001 |
464 |
28 |
1,082,076,419 |
3 |
9 |
220 | |
473 |
752 |
852 |
880 |
|
3924 |
3439 |
2687 |
752 |
25 |
2,188,418,573 |
3 |
10 |
286 | |
829 |
1160 |
1303 |
1320 |
|
4896 |
4641 |
3481 |
1160 |
21 |
4,295,198,359 |
3 |
11 |
364 | |
1329 |
1712 |
1906 |
1904 |
|
5976 |
6095 |
4383 |
1712 |
19 |
7,307,001,243 |
3 |
12 |
455 | |
1997 |
2432 |
2685 |
2656 |
|
7164 |
7801 |
5393 |
2408 |
16 |
12,039,692,540 |
3 |
13 |
560 | |
2857 |
3344 |
3664 |
3600 |
|
8460 |
9759 |
6511 |
3248 |
15 |
19,304,622,019 |
3 |
14 |
680 | |
3933 |
4472 |
4867 |
4760 |
|
9864 |
11969 |
7737 |
4232 |
13 |
29,198,372,952 |
3 |
15 |
816 | |
5249 |
5840 |
6318 |
6160 |
|
11376 |
14431 |
9071 |
5360 |
12 |
43,046,179,367 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
720 |
369 |
334 |
35 |
72 |
18,152,634 |
4 |
5 |
56 | |
23 |
62 |
64 |
67 |
|
1224 |
671 |
609 |
62 |
67 |
95,196,953 |
4 |
6 |
84 | |
4 |
108 |
116 |
128 |
|
1872 |
1105 |
997 |
108 |
69 |
382,054,051 |
4 |
7 |
120 | |
-2 |
184 |
203 |
230 |
|
2664 |
1695 |
1511 |
184 |
67 |
1,209,255,146 |
4 |
8 |
165 | |
28 |
305 |
342 |
385 |
|
3600 |
2465 |
2160 |
305 |
48 |
3,117,844,012 |
4 |
9 |
220 | |
118 |
487 |
551 |
605 |
|
4680 |
3439 |
2952 |
487 |
56 |
6,478,672,602 |
4 |
10 |
286 | |
292 |
753 |
854 |
913 |
|
5904 |
4641 |
3888 |
753 |
50 |
12,864,898,758 |
4 |
11 |
364 | |
574 |
1127 |
1275 |
1332 |
|
7272 |
6095 |
4968 |
1127 |
37 |
24,907,652,916 |
4 |
12 |
455 | |
988 |
1633 |
1838 |
1885 |
|
8784 |
7825 |
6192 |
1633 |
33 |
43,442,916,847 |
4 |
13 |
560 | |
1558 |
2295 |
2567 |
2595 |
|
10440 |
9855 |
7560 |
2295 |
29 |
68,139,581,912 |
4 |
14 |
680 | |
2308 |
3137 |
3486 |
3485 |
|
12240 |
12209 |
9072 |
3137 |
26 |
108,297,691,571 |
4 |
15 |
816 | |
3262 |
4183 |
4619 |
4579 |
|
14184 |
14887 |
10728 |
4159 |
24 |
168,322,906,470 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1260 |
671 |
615 |
56 |
78 |
108,017,291 |
5 |
6 |
84 | |
40 |
90 |
92 |
95 |
|
1980 |
1105 |
1015 |
90 |
81 |
482,042,778 |
5 |
7 |
120 | |
7 |
144 |
152 |
164 |
|
2880 |
1695 |
1551 |
144 |
82 |
1,637,661,477 |
5 |
8 |
165 | |
-23 |
225 |
245 |
275 |
|
3960 |
2465 |
2240 |
225 |
76 |
4,842,428,852 |
5 |
9 |
220 | |
-29 |
348 |
386 |
440 |
|
5220 |
3439 |
3091 |
348 |
73 |
12,065,316,884 |
5 |
10 |
286 | |
13 |
528 |
593 |
671 |
|
6660 |
4641 |
4113 |
528 |
67 |
26,240,756,349 |
5 |
11 |
364 | |
127 |
780 |
884 |
980 |
|
8280 |
6095 |
5315 |
780 |
65 |
45,586,704,830 |
5 |
12 |
455 | |
337 |
1128 |
1283 |
1390 |
|
10080 |
7825 |
6697 |
1128 |
64 |
80,786,089,682 |
5 |
13 |
560 | |
667 |
1596 |
1814 |
1924 |
|
12060 |
9855 |
8259 |
1596 |
58 |
141,664,894,065 |
5 |
14 |
680 | |
1141 |
2208 |
2501 |
2605 |
|
14220 |
12209 |
10001 |
2208 |
43 |
214,122,340,455 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2016 |
1105 |
1021 |
84 |
85 |
526,806,986 |
6 |
7 |
120 | |
65 |
126 |
128 |
131 |
|
2988 |
1695 |
1569 |
126 |
88 |
1,845,362,893 |
6 |
8 |
165 | |
19 |
189 |
197 |
209 |
|
4176 |
2465 |
2276 |
189 |
83 |
5,682,861,919 |
6 |
9 |
220 | |
-34 |
280 |
300 |
330 |
|
5580 |
3439 |
3159 |
280 |
79 |
14,133,327,050 |
6 |
10 |
286 | |
-74 |
410 |
449 |
506 |
|
7200 |
4641 |
4231 |
410 |
76 |
32,380,209,837 |
6 |
11 |
364 | |
-78 |
594 |
660 |
749 |
|
9036 |
6095 |
5501 |
594 |
73 |
66,803,607,041 |
6 |
12 |
455 | |
-22 |
847 |
951 |
1071 |
|
11088 |
7825 |
6978 |
847 |
74 |
132,451,524,938 |
6 |
13 |
560 | |
118 |
1185 |
1340 |
1484 |
|
13356 |
9855 |
8670 |
1185 |
71 |
227,815,450,740 |
6 |
14 |
680 | |
366 |
1631 |
1851 |
2011 |
|
15840 |
12209 |
10578 |
1631 |
67 |
385,965,882,699 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3024 |
1695 |
1575 |
120 |
91 |
1,935,564,244 |
7 |
8 |
165 | |
99 |
171 |
173 |
176 |
|
4284 |
2465 |
2294 |
171 |
90 |
5,970,161,115 |
7 |
9 |
220 | |
41 |
244 |
252 |
264 |
|
5796 |
3439 |
3195 |
244 |
87 |
15,904,274,584 |
7 |
10 |
286 | |
-34 |
346 |
366 |
396 |
|
7560 |
4641 |
4295 |
346 |
83 |
36,875,568,442 |
7 |
11 |
364 | |
-106 |
484 |
524 |
584 |
|
9576 |
6095 |
5611 |
484 |
82 |
82,203,191,769 |
7 |
12 |
455 | |
-154 |
673 |
741 |
840 |
|
11844 |
7825 |
7152 |
673 |
83 |
174,360,001,076 |
7 |
13 |
560 | |
-154 |
928 |
1034 |
1176 |
|
14364 |
9855 |
8927 |
928 |
81 |
317,154,696,055 |
7 |
14 |
680 | |
-82 |
1264 |
1421 |
1604 |
|
17136 |
12209 |
10945 |
1264 |
78 |
538,273,640,533 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4320 |
2465 |
2300 |
165 |
90 |
6,159,558,290 |
8 |
9 |
220 | |
143 |
226 |
228 |
231 |
|
5904 |
3439 |
3213 |
226 |
89 |
17,009,668,138 |
8 |
10 |
286 | |
74 |
310 |
318 |
330 |
|
7776 |
4641 |
4331 |
310 |
88 |
40,604,827,603 |
8 |
11 |
364 | |
-22 |
424 |
444 |
474 |
|
9936 |
6095 |
5671 |
424 |
88 |
96,032,165,892 |
8 |
12 |
455 | |
-125 |
575 |
615 |
675 |
|
12384 |
7825 |
7250 |
575 |
88 |
187,846,769,096 |
8 |
13 |
560 | |
-215 |
774 |
843 |
945 |
|
15120 |
9855 |
9081 |
774 |
84 |
348,307,099,164 |
8 |
14 |
680 | |
-269 |
1036 |
1143 |
1296 |
|
18144 |
12209 |
11173 |
1036 |
85 |
657,557,042,788 |
|
Bounds and Dimensions on the regular type-IV Split
shelling parameters: a0 = 1 a1 = 11 a2 = 11 a3 = 1
Combinatorics:
24 | tetrahedra |
36 | interior faces |
14 | interior edges |
1 | interior vertices |
| |
24 | boundary faces |
36 | boundary edges |
14 | boundary vertices |
| |
60 | faces total |
50 | edges total |
15 | vertices total |