Bounds and Dimensions on the Morgan-Scott 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 |
84 |
10,685 |
1 |
2 |
10 | |
10 |
14 |
14 |
23 |
|
126 |
75 |
61 |
14 |
60 |
282,525 |
1 |
3 |
20 | |
44 |
48 |
53 |
72 |
|
252 |
203 |
155 |
48 |
53 |
1,958,148 |
1 |
4 |
35 | |
134 |
138 |
149 |
178 |
|
420 |
429 |
291 |
138 |
46 |
7,715,152 |
1 |
5 |
56 | |
308 |
312 |
330 |
368 |
|
630 |
781 |
469 |
312 |
28 |
25,951,001 |
1 |
6 |
84 | |
594 |
598 |
624 |
670 |
|
882 |
1259 |
689 |
570 |
50 |
71,406,890 |
1 |
7 |
120 | |
1020 |
1024 |
1059 |
1112 |
|
1176 |
1863 |
951 |
912 |
35 |
165,014,120 |
1 |
8 |
165 | |
1614 |
1618 |
1663 |
1722 |
|
1512 |
2593 |
1255 |
1338 |
52 |
341,178,310 |
1 |
9 |
220 | |
2404 |
2408 |
2464 |
2528 |
|
1890 |
3449 |
1601 |
1848 |
40 |
634,641,101 |
1 |
10 |
286 | |
3418 |
3422 |
3490 |
3558 |
|
2310 |
4431 |
1989 |
2442 |
52 |
1,118,791,538 |
1 |
11 |
364 | |
4684 |
4688 |
4769 |
4840 |
|
2772 |
5539 |
2419 |
3120 |
42 |
1,835,198,545 |
1 |
12 |
455 | |
6230 |
6234 |
6329 |
6402 |
|
3276 |
6773 |
2891 |
3882 |
52 |
2,871,507,428 |
1 |
13 |
560 | |
8084 |
8088 |
8198 |
8272 |
|
3822 |
8133 |
3405 |
4728 |
44 |
4,410,362,343 |
1 |
14 |
680 | |
10274 |
10278 |
10404 |
10478 |
|
4410 |
9619 |
3961 |
5658 |
52 |
6,489,283,084 |
1 |
15 |
816 | |
12828 |
12832 |
12975 |
13048 |
|
5040 |
11231 |
4559 |
6672 |
44 |
9,318,063,372 |
1 |
16 |
969 | |
15774 |
15778 |
15939 |
16010 |
|
5712 |
12969 |
5199 |
7770 |
52 |
12,816,799,881 |
1 |
17 |
1140 | |
19140 |
19144 |
19324 |
19392 |
|
6426 |
14833 |
5881 |
8952 |
45 |
17,478,972,822 |
1 |
18 |
1330 | |
22954 |
22958 |
23158 |
23222 |
|
7182 |
16823 |
6605 |
10218 |
51 |
23,377,042,285 |
1 |
19 |
1540 | |
27244 |
27248 |
27469 |
27528 |
|
7980 |
18939 |
7371 |
11568 |
46 |
31,562,641,238 |
1 |
20 |
1771 | |
32038 |
32042 |
32285 |
32338 |
|
8820 |
21181 |
8179 |
13002 |
51 |
40,515,460,351 |
1 |
21 |
2024 | |
37364 |
37368 |
37634 |
37680 |
|
9702 |
23549 |
9029 |
14520 |
46 |
52,505,162,181 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
168 |
75 |
65 |
10 |
81 |
416,735 |
2 |
3 |
20 | |
7 |
20 |
20 |
33 |
|
378 |
203 |
183 |
20 |
90 |
3,319,192 |
2 |
4 |
35 | |
19 |
39 |
46 |
87 |
|
672 |
429 |
390 |
39 |
90 |
19,157,749 |
2 |
5 |
56 | |
73 |
94 |
116 |
186 |
|
1050 |
781 |
687 |
94 |
84 |
81,278,238 |
2 |
6 |
84 | |
197 |
218 |
258 |
357 |
|
1512 |
1287 |
1069 |
218 |
51 |
271,195,232 |
2 |
7 |
120 | |
419 |
440 |
500 |
627 |
|
2058 |
1975 |
1535 |
440 |
36 |
702,353,782 |
2 |
8 |
165 | |
767 |
788 |
870 |
1023 |
|
2688 |
2873 |
2085 |
788 |
29 |
1,697,895,496 |
2 |
9 |
220 | |
1269 |
1290 |
1396 |
1573 |
|
3402 |
3981 |
2719 |
1262 |
25 |
3,667,889,489 |
2 |
10 |
286 | |
1953 |
1974 |
2106 |
2305 |
|
4200 |
5299 |
3437 |
1862 |
23 |
7,063,893,321 |
2 |
11 |
364 | |
2847 |
2868 |
3028 |
3247 |
|
5082 |
6827 |
4239 |
2588 |
21 |
12,716,299,765 |
2 |
12 |
455 | |
3979 |
4000 |
4190 |
4427 |
|
6048 |
8565 |
5125 |
3440 |
20 |
22,531,716,927 |
2 |
13 |
560 | |
5377 |
5398 |
5620 |
5873 |
|
7098 |
10513 |
6095 |
4418 |
19 |
38,128,535,700 |
2 |
14 |
680 | |
7069 |
7090 |
7346 |
7613 |
|
8232 |
12671 |
7149 |
5522 |
19 |
55,759,970,550 |
2 |
15 |
816 | |
9083 |
9104 |
9396 |
9675 |
|
9450 |
15039 |
8287 |
6752 |
18 |
87,981,807,420 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
420 |
203 |
183 |
20 |
90 |
4,013,377 |
3 |
4 |
35 | |
9 |
35 |
35 |
48 |
|
798 |
429 |
394 |
35 |
85 |
27,720,272 |
3 |
5 |
56 | |
1 |
56 |
56 |
108 |
|
1302 |
781 |
725 |
56 |
90 |
138,502,852 |
3 |
6 |
84 | |
21 |
95 |
108 |
214 |
|
1932 |
1287 |
1192 |
95 |
92 |
490,330,645 |
3 |
7 |
120 | |
97 |
183 |
219 |
380 |
|
2688 |
1975 |
1792 |
183 |
94 |
1,369,295,756 |
3 |
8 |
165 | |
257 |
355 |
417 |
633 |
|
3570 |
2873 |
2518 |
355 |
95 |
3,177,021,321 |
3 |
9 |
220 | |
529 |
639 |
730 |
1000 |
|
4578 |
4009 |
3370 |
639 |
95 |
6,842,726,695 |
3 |
10 |
286 | |
941 |
1063 |
1186 |
1508 |
|
5712 |
5411 |
4348 |
1063 |
95 |
14,073,006,026 |
3 |
11 |
364 | |
1521 |
1655 |
1813 |
2184 |
|
6972 |
7107 |
5452 |
1655 |
95 |
26,587,166,576 |
3 |
12 |
455 | |
2297 |
2443 |
2639 |
3056 |
|
8358 |
9097 |
6682 |
2415 |
96 |
47,515,264,703 |
3 |
13 |
560 | |
3297 |
3455 |
3692 |
4152 |
|
9870 |
11381 |
8038 |
3343 |
96 |
78,000,483,023 |
3 |
14 |
680 | |
4549 |
4719 |
5000 |
5500 |
|
11508 |
13959 |
9520 |
4439 |
96 |
128,433,423,219 |
3 |
15 |
816 | |
6081 |
6263 |
6591 |
7128 |
|
13272 |
16831 |
11128 |
5703 |
97 |
206,501,257,413 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
840 |
429 |
394 |
35 |
85 |
32,252,618 |
4 |
5 |
56 | |
17 |
56 |
56 |
69 |
|
1428 |
781 |
725 |
56 |
90 |
173,421,838 |
4 |
6 |
84 | |
-10 |
84 |
84 |
136 |
|
2184 |
1287 |
1203 |
84 |
92 |
724,718,341 |
4 |
7 |
120 | |
-22 |
121 |
130 |
250 |
|
3108 |
1975 |
1854 |
121 |
99 |
2,469,608,742 |
4 |
8 |
165 | |
8 |
183 |
222 |
425 |
|
4200 |
2873 |
2690 |
183 |
99 |
6,431,106,837 |
4 |
9 |
220 | |
108 |
308 |
388 |
675 |
|
5460 |
4009 |
3701 |
308 |
96 |
14,025,190,315 |
4 |
10 |
286 | |
306 |
530 |
656 |
1027 |
|
6888 |
5411 |
4881 |
530 |
92 |
29,689,119,789 |
4 |
11 |
364 | |
630 |
878 |
1054 |
1508 |
|
8484 |
7107 |
6229 |
878 |
87 |
59,509,239,933 |
4 |
12 |
455 | |
1108 |
1380 |
1610 |
2145 |
|
10248 |
9125 |
7745 |
1380 |
61 |
107,095,690,013 |
4 |
13 |
560 | |
1768 |
2064 |
2352 |
2965 |
|
12180 |
11493 |
9429 |
2064 |
60 |
178,104,278,164 |
4 |
14 |
680 | |
2638 |
2958 |
3308 |
3995 |
|
14280 |
14239 |
11281 |
2958 |
58 |
301,443,345,545 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1470 |
781 |
725 |
56 |
90 |
178,776,748 |
5 |
6 |
84 | |
32 |
84 |
84 |
97 |
|
2310 |
1287 |
1203 |
84 |
92 |
833,684,122 |
5 |
7 |
120 | |
-13 |
120 |
120 |
172 |
|
3360 |
1975 |
1855 |
120 |
99 |
2,921,064,593 |
5 |
8 |
165 | |
-55 |
165 |
165 |
295 |
|
4620 |
2873 |
2708 |
165 |
99 |
9,036,943,590 |
5 |
9 |
220 | |
-69 |
221 |
243 |
480 |
|
6090 |
4009 |
3788 |
221 |
96 |
21,668,692,140 |
5 |
10 |
286 | |
-27 |
311 |
382 |
741 |
|
7770 |
5411 |
5100 |
311 |
98 |
47,270,021,612 |
5 |
11 |
364 | |
99 |
477 |
610 |
1092 |
|
9660 |
7107 |
6630 |
477 |
98 |
92,723,107,975 |
5 |
12 |
455 | |
337 |
755 |
955 |
1560 |
|
11760 |
9125 |
8370 |
755 |
97 |
171,286,953,403 |
5 |
13 |
560 | |
715 |
1173 |
1445 |
2172 |
|
14070 |
11493 |
10320 |
1173 |
98 |
293,161,746,599 |
5 |
14 |
680 | |
1261 |
1759 |
2108 |
2955 |
|
16590 |
14239 |
12480 |
1759 |
98 |
463,935,063,305 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2352 |
1287 |
1203 |
84 |
92 |
861,934,645 |
6 |
7 |
120 | |
55 |
120 |
120 |
133 |
|
3486 |
1975 |
1855 |
120 |
99 |
3,243,289,010 |
6 |
8 |
165 | |
-7 |
165 |
165 |
217 |
|
4872 |
2873 |
2708 |
165 |
99 |
10,050,328,698 |
6 |
9 |
220 | |
-78 |
220 |
220 |
350 |
|
6510 |
4009 |
3789 |
220 |
96 |
25,899,483,827 |
6 |
10 |
286 | |
-134 |
286 |
295 |
546 |
|
8400 |
5411 |
5125 |
286 |
98 |
56,199,135,364 |
6 |
11 |
364 | |
-148 |
369 |
418 |
819 |
|
10542 |
7107 |
6738 |
369 |
99 |
115,767,439,512 |
6 |
12 |
455 | |
-92 |
501 |
617 |
1183 |
|
12936 |
9125 |
8624 |
501 |
99 |
220,590,652,575 |
6 |
13 |
560 | |
62 |
724 |
920 |
1652 |
|
15582 |
11493 |
10769 |
724 |
99 |
382,948,551,588 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3528 |
1975 |
1855 |
120 |
99 |
3,307,701,494 |
7 |
8 |
165 | |
87 |
165 |
165 |
178 |
|
4998 |
2873 |
2708 |
165 |
99 |
10,624,472,685 |
7 |
9 |
220 | |
9 |
220 |
220 |
272 |
|
6762 |
4009 |
3789 |
220 |
96 |
27,054,370,499 |
7 |
10 |
286 | |
-90 |
286 |
286 |
416 |
|
8820 |
5411 |
5125 |
286 |
98 |
64,561,703,734 |
7 |
11 |
364 | |
-186 |
364 |
364 |
624 |
|
11172 |
7107 |
6743 |
364 |
99 |
131,609,878,013 |
7 |
12 |
455 | |
-254 |
455 |
477 |
910 |
|
13818 |
9125 |
8670 |
455 |
99 |
263,487,874,071 |
7 |
13 |
560 | |
-266 |
568 |
653 |
1288 |
|
16758 |
11493 |
10925 |
568 |
99 |
510,379,285,642 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
5040 |
2873 |
2708 |
165 |
99 |
10,584,405,780 |
8 |
9 |
220 | |
129 |
220 |
220 |
233 |
|
6888 |
4009 |
3789 |
220 |
96 |
28,074,446,015 |
8 |
10 |
286 | |
36 |
286 |
286 |
338 |
|
9072 |
5411 |
5125 |
286 |
98 |
68,700,568,600 |
8 |
11 |
364 | |
-90 |
364 |
364 |
494 |
|
11592 |
7107 |
6743 |
364 |
99 |
147,691,332,755 |
8 |
12 |
455 | |
-225 |
455 |
455 |
715 |
|
14448 |
9125 |
8670 |
455 |
99 |
313,263,505,110 |
8 |
13 |
560 | |
-345 |
560 |
568 |
1015 |
|
17640 |
11493 |
10933 |
560 |
99 |
593,824,831,411 |
|
Bounds and Dimensions on the Morgan-Scott 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 |