Bounds and Dimensions on the Wang-MS Split of Faces
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 |
|
42 |
17 |
13 |
4 |
86 |
9,060 |
1 |
2 |
10 | |
10 |
10 |
10 |
23 |
|
126 |
75 |
65 |
10 |
74 |
277,215 |
1 |
3 |
20 | |
44 |
44 |
45 |
72 |
|
252 |
203 |
159 |
44 |
19 |
1,247,455 |
1 |
4 |
35 | |
134 |
134 |
137 |
178 |
|
420 |
429 |
295 |
134 |
8 |
4,582,475 |
1 |
5 |
56 | |
308 |
308 |
314 |
368 |
|
630 |
781 |
473 |
308 |
4 |
13,627,668 |
1 |
6 |
84 | |
594 |
594 |
604 |
670 |
|
882 |
1259 |
693 |
566 |
3 |
33,567,916 |
1 |
7 |
120 | |
1020 |
1020 |
1035 |
1112 |
|
1176 |
1863 |
955 |
908 |
2 |
71,843,084 |
1 |
8 |
165 | |
1614 |
1614 |
1635 |
1722 |
|
1512 |
2593 |
1259 |
1334 |
2 |
139,133,010 |
1 |
9 |
220 | |
2404 |
2404 |
2432 |
2528 |
|
1890 |
3449 |
1605 |
1844 |
1 |
249,884,110 |
1 |
10 |
286 | |
3418 |
3418 |
3454 |
3558 |
|
2310 |
4431 |
1993 |
2438 |
1 |
424,259,777 |
1 |
11 |
364 | |
4684 |
4684 |
4729 |
4840 |
|
2772 |
5539 |
2423 |
3116 |
1 |
678,256,350 |
1 |
12 |
455 | |
6230 |
6230 |
6285 |
6402 |
|
3276 |
6773 |
2895 |
3878 |
1 |
1,042,731,052 |
1 |
13 |
560 | |
8084 |
8084 |
8150 |
8272 |
|
3822 |
8133 |
3409 |
4724 |
1 |
1,554,062,483 |
1 |
14 |
680 | |
10274 |
10274 |
10352 |
10478 |
|
4410 |
9619 |
3965 |
5654 |
1 |
2,239,766,283 |
1 |
15 |
816 | |
12828 |
12828 |
12919 |
13048 |
|
5040 |
11231 |
4563 |
6668 |
1 |
3,142,907,845 |
1 |
16 |
969 | |
15774 |
15774 |
15879 |
16010 |
|
5712 |
12969 |
5203 |
7766 |
1 |
4,365,847,361 |
1 |
17 |
1140 | |
19140 |
19140 |
19260 |
19392 |
|
6426 |
14833 |
5885 |
8948 |
1 |
5,846,632,155 |
1 |
18 |
1330 | |
22954 |
22954 |
23090 |
23222 |
|
7182 |
16823 |
6609 |
10214 |
1 |
7,812,578,197 |
1 |
19 |
1540 | |
27244 |
27244 |
27397 |
27528 |
|
7980 |
18939 |
7375 |
11564 |
1 |
10,215,859,577 |
1 |
20 |
1771 | |
32038 |
32038 |
32209 |
32338 |
|
8820 |
21181 |
8183 |
12998 |
1 |
13,132,793,979 |
1 |
21 |
2024 | |
37364 |
37364 |
37554 |
37680 |
|
9702 |
23549 |
9033 |
14516 |
1 |
16,756,856,746 |
1 |
22 |
2300 | |
43250 |
43250 |
43582 |
43582 |
|
10626 |
26043 |
9925 |
16118 |
1 |
21,154,973,609 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
168 |
75 |
65 |
10 |
74 |
376,362 |
2 |
3 |
20 | |
7 |
20 |
20 |
33 |
|
378 |
203 |
183 |
20 |
77 |
3,152,138 |
2 |
4 |
35 | |
19 |
44 |
46 |
87 |
|
672 |
429 |
385 |
44 |
82 |
15,972,423 |
2 |
5 |
56 | |
73 |
110 |
116 |
186 |
|
1050 |
781 |
671 |
110 |
41 |
55,675,588 |
2 |
6 |
84 | |
197 |
246 |
258 |
357 |
|
1512 |
1287 |
1041 |
246 |
24 |
147,600,094 |
2 |
7 |
120 | |
419 |
480 |
500 |
627 |
|
2058 |
1975 |
1495 |
480 |
15 |
357,368,788 |
2 |
8 |
165 | |
767 |
840 |
870 |
1023 |
|
2688 |
2873 |
2033 |
840 |
10 |
751,528,468 |
2 |
9 |
220 | |
1269 |
1354 |
1396 |
1573 |
|
3402 |
3981 |
2655 |
1326 |
7 |
1,447,694,264 |
2 |
10 |
286 | |
1953 |
2050 |
2106 |
2305 |
|
4200 |
5299 |
3361 |
1938 |
6 |
2,563,893,468 |
2 |
11 |
364 | |
2847 |
2956 |
3028 |
3247 |
|
5082 |
6827 |
4151 |
2676 |
5 |
4,301,447,187 |
2 |
12 |
455 | |
3979 |
4100 |
4190 |
4427 |
|
6048 |
8565 |
5025 |
3540 |
4 |
6,818,022,729 |
2 |
13 |
560 | |
5377 |
5510 |
5620 |
5873 |
|
7098 |
10513 |
5983 |
4530 |
3 |
11,114,477,938 |
2 |
14 |
680 | |
7069 |
7214 |
7346 |
7613 |
|
8232 |
12671 |
7025 |
5646 |
3 |
15,403,377,064 |
2 |
15 |
816 | |
9083 |
9240 |
9396 |
9675 |
|
9450 |
15039 |
8151 |
6888 |
3 |
22,207,267,126 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
420 |
203 |
183 |
20 |
77 |
4,310,006 |
3 |
4 |
35 | |
9 |
35 |
35 |
48 |
|
798 |
429 |
394 |
35 |
83 |
26,838,540 |
3 |
5 |
56 | |
1 |
56 |
56 |
108 |
|
1302 |
781 |
725 |
56 |
85 |
124,019,194 |
3 |
6 |
84 | |
21 |
100 |
108 |
214 |
|
1932 |
1287 |
1187 |
100 |
84 |
376,496,560 |
3 |
7 |
120 | |
97 |
200 |
219 |
380 |
|
2688 |
1975 |
1775 |
200 |
74 |
882,167,982 |
3 |
8 |
165 | |
257 |
384 |
417 |
633 |
|
3570 |
2873 |
2489 |
384 |
56 |
2,090,552,197 |
3 |
9 |
220 | |
529 |
680 |
730 |
1000 |
|
4578 |
4009 |
3329 |
680 |
43 |
3,886,245,730 |
3 |
10 |
286 | |
941 |
1116 |
1186 |
1508 |
|
5712 |
5411 |
4295 |
1116 |
34 |
6,878,058,873 |
3 |
11 |
364 | |
1521 |
1720 |
1813 |
2184 |
|
6972 |
7107 |
5387 |
1720 |
28 |
12,119,845,853 |
3 |
12 |
455 | |
2297 |
2520 |
2639 |
3056 |
|
8358 |
9097 |
6605 |
2492 |
23 |
22,203,288,841 |
3 |
13 |
560 | |
3297 |
3544 |
3692 |
4152 |
|
9870 |
11381 |
7949 |
3432 |
17 |
31,558,073,793 |
3 |
14 |
680 | |
4549 |
4820 |
5000 |
5500 |
|
11508 |
13959 |
9419 |
4540 |
15 |
46,996,032,304 |
3 |
15 |
816 | |
6081 |
6376 |
6591 |
7128 |
|
13272 |
16831 |
11015 |
5816 |
14 |
72,680,266,495 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
840 |
429 |
394 |
35 |
83 |
33,532,758 |
4 |
5 |
56 | |
17 |
56 |
56 |
69 |
|
1428 |
781 |
725 |
56 |
85 |
162,646,366 |
4 |
6 |
84 | |
-10 |
84 |
84 |
136 |
|
2184 |
1287 |
1203 |
84 |
87 |
661,723,837 |
4 |
7 |
120 | |
-22 |
120 |
130 |
250 |
|
3108 |
1975 |
1855 |
120 |
95 |
2,114,940,259 |
4 |
8 |
165 | |
8 |
198 |
222 |
425 |
|
4200 |
2873 |
2675 |
198 |
91 |
4,993,805,679 |
4 |
9 |
220 | |
108 |
346 |
388 |
675 |
|
5460 |
4009 |
3663 |
346 |
82 |
10,728,230,528 |
4 |
10 |
286 | |
306 |
592 |
656 |
1027 |
|
6888 |
5411 |
4819 |
592 |
70 |
20,672,279,788 |
4 |
11 |
364 | |
630 |
964 |
1054 |
1508 |
|
8484 |
7107 |
6143 |
964 |
49 |
37,630,588,874 |
4 |
12 |
455 | |
1108 |
1490 |
1610 |
2145 |
|
10248 |
9125 |
7635 |
1490 |
36 |
57,545,776,891 |
4 |
13 |
560 | |
1768 |
2198 |
2352 |
2965 |
|
12180 |
11493 |
9295 |
2198 |
28 |
97,255,905,141 |
4 |
14 |
680 | |
2638 |
3116 |
3308 |
3995 |
|
14280 |
14239 |
11123 |
3116 |
22 |
159,514,362,384 |
4 |
15 |
816 | |
3746 |
4272 |
5263 |
5263 |
|
16548 |
17363 |
13119 |
4244 |
17 |
233,061,181,895 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1470 |
781 |
725 |
56 |
85 |
180,087,277 |
5 |
6 |
84 | |
32 |
84 |
84 |
97 |
|
2310 |
1287 |
1203 |
84 |
87 |
800,449,309 |
5 |
7 |
120 | |
-13 |
120 |
120 |
172 |
|
3360 |
1975 |
1855 |
120 |
95 |
2,796,692,773 |
5 |
8 |
165 | |
-55 |
165 |
165 |
295 |
|
4620 |
2873 |
2708 |
165 |
87 |
8,041,168,329 |
5 |
9 |
220 | |
-69 |
224 |
243 |
480 |
|
6090 |
4009 |
3785 |
224 |
91 |
18,528,454,864 |
5 |
10 |
286 | |
-27 |
338 |
382 |
741 |
|
7770 |
5411 |
5073 |
338 |
88 |
36,504,375,813 |
5 |
11 |
364 | |
99 |
536 |
610 |
1092 |
|
9660 |
7107 |
6571 |
536 |
83 |
69,344,961,197 |
5 |
12 |
455 | |
337 |
846 |
955 |
1560 |
|
11760 |
9125 |
8279 |
846 |
74 |
116,096,834,314 |
5 |
13 |
560 | |
715 |
1296 |
1445 |
2172 |
|
14070 |
11493 |
10197 |
1296 |
61 |
179,264,274,475 |
5 |
14 |
680 | |
1261 |
1914 |
2108 |
2955 |
|
16590 |
14239 |
12325 |
1914 |
51 |
276,070,344,090 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2352 |
1287 |
1203 |
84 |
87 |
865,195,669 |
6 |
7 |
120 | |
55 |
120 |
120 |
133 |
|
3486 |
1975 |
1855 |
120 |
95 |
3,291,665,503 |
6 |
8 |
165 | |
-7 |
165 |
165 |
217 |
|
4872 |
2873 |
2708 |
165 |
87 |
9,592,446,387 |
6 |
9 |
220 | |
-78 |
220 |
220 |
350 |
|
6510 |
4009 |
3789 |
220 |
89 |
24,042,018,122 |
6 |
10 |
286 | |
-134 |
286 |
295 |
546 |
|
8400 |
5411 |
5125 |
286 |
92 |
48,999,664,967 |
6 |
11 |
364 | |
-148 |
380 |
418 |
819 |
|
10542 |
7107 |
6727 |
380 |
95 |
92,852,434,524 |
6 |
12 |
455 | |
-92 |
544 |
617 |
1183 |
|
12936 |
9125 |
8581 |
544 |
95 |
178,253,426,305 |
6 |
13 |
560 | |
62 |
806 |
920 |
1652 |
|
15582 |
11493 |
10687 |
806 |
91 |
296,935,765,840 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3528 |
1975 |
1855 |
120 |
95 |
3,405,473,626 |
7 |
8 |
165 | |
87 |
165 |
165 |
178 |
|
4998 |
2873 |
2708 |
165 |
87 |
10,600,209,225 |
7 |
9 |
220 | |
9 |
220 |
220 |
272 |
|
6762 |
4009 |
3789 |
220 |
89 |
26,566,449,446 |
7 |
10 |
286 | |
-90 |
286 |
286 |
416 |
|
8820 |
5411 |
5125 |
286 |
92 |
59,635,806,344 |
7 |
11 |
364 | |
-186 |
364 |
364 |
624 |
|
11172 |
7107 |
6743 |
364 |
96 |
120,584,540,620 |
7 |
12 |
455 | |
-254 |
455 |
477 |
910 |
|
13818 |
9125 |
8670 |
455 |
96 |
231,354,295,713 |
7 |
13 |
560 | |
-266 |
587 |
653 |
1288 |
|
16758 |
11493 |
10906 |
587 |
94 |
404,555,401,716 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
5040 |
2873 |
2708 |
165 |
87 |
11,219,718,150 |
8 |
9 |
220 | |
129 |
220 |
220 |
233 |
|
6888 |
4009 |
3789 |
220 |
89 |
29,531,338,325 |
8 |
10 |
286 | |
36 |
286 |
286 |
338 |
|
9072 |
5411 |
5125 |
286 |
92 |
66,329,403,020 |
8 |
11 |
364 | |
-90 |
364 |
364 |
494 |
|
11592 |
7107 |
6743 |
364 |
96 |
138,641,330,044 |
8 |
12 |
455 | |
-225 |
455 |
455 |
715 |
|
14448 |
9125 |
8670 |
455 |
96 |
271,716,571,659 |
8 |
13 |
560 | |
-345 |
560 |
568 |
1015 |
|
17640 |
11493 |
10933 |
560 |
95 |
514,686,523,596 |
|
Bounds and Dimensions on the Wang-MS Split of Faces
shelling parameters: a0 = 1 a1 = 13 a2 = 13 a3 = 1
Combinatorics:
28 | tetrahedra |
42 | interior faces |
16 | interior edges |
1 | interior vertices |
| |
28 | boundary faces |
42 | boundary edges |
16 | boundary vertices |
| |
70 | faces total |
58 | edges total |
17 | vertices total |