Bounds and Dimensions on the generic Morgan-Scott 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 |
|
28 |
8 |
4 |
4 |
100 |
1,735 |
1 |
2 |
10 | |
8 |
10 |
10 |
14 |
|
84 |
32 |
22 |
10 |
61 |
94,267 |
1 |
3 |
20 | |
16 |
20 |
20 |
36 |
|
168 |
88 |
68 |
20 |
47 |
482,161 |
1 |
4 |
35 | |
43 |
43 |
49 |
81 |
|
280 |
191 |
148 |
43 |
73 |
2,403,988 |
1 |
5 |
56 | |
104 |
104 |
112 |
160 |
|
420 |
356 |
252 |
104 |
76 |
9,775,739 |
1 |
6 |
84 | |
214 |
214 |
224 |
288 |
|
588 |
594 |
384 |
210 |
76 |
31,628,631 |
1 |
7 |
120 | |
388 |
388 |
400 |
480 |
|
784 |
916 |
544 |
372 |
76 |
85,053,285 |
1 |
8 |
165 | |
641 |
641 |
655 |
751 |
|
1008 |
1322 |
732 |
590 |
76 |
194,254,070 |
1 |
9 |
220 | |
988 |
988 |
1004 |
1116 |
|
1260 |
1812 |
948 |
864 |
75 |
396,273,331 |
1 |
10 |
286 | |
1444 |
1444 |
1462 |
1590 |
|
1540 |
2386 |
1192 |
1194 |
75 |
742,046,105 |
1 |
11 |
364 | |
2024 |
2024 |
2044 |
2188 |
|
1848 |
3044 |
1464 |
1580 |
75 |
1,289,479,781 |
1 |
12 |
455 | |
2743 |
2743 |
2765 |
2925 |
|
2184 |
3786 |
1764 |
2022 |
74 |
2,137,595,192 |
1 |
13 |
560 | |
3616 |
3616 |
3640 |
3816 |
|
2548 |
4612 |
2092 |
2520 |
74 |
3,382,730,821 |
1 |
14 |
680 | |
4658 |
4658 |
4684 |
4876 |
|
2940 |
5522 |
2448 |
3074 |
74 |
5,106,938,207 |
1 |
15 |
816 | |
5884 |
5884 |
5912 |
6120 |
|
3360 |
6516 |
2832 |
3684 |
74 |
7,429,468,710 |
1 |
16 |
969 | |
7309 |
7309 |
7339 |
7563 |
|
3808 |
7594 |
3244 |
4350 |
74 |
10,573,339,797 |
1 |
17 |
1140 | |
8948 |
8948 |
8980 |
9220 |
|
4284 |
8756 |
3684 |
5072 |
74 |
14,724,377,042 |
1 |
18 |
1330 | |
10816 |
10816 |
10850 |
11106 |
|
4788 |
10002 |
4152 |
5850 |
73 |
20,244,731,137 |
1 |
19 |
1540 | |
12928 |
12928 |
12964 |
13236 |
|
5320 |
11332 |
4648 |
6684 |
73 |
27,345,419,171 |
1 |
20 |
1771 | |
15299 |
15299 |
15337 |
15625 |
|
5880 |
12746 |
5172 |
7574 |
73 |
35,795,202,845 |
1 |
21 |
2024 | |
17944 |
17944 |
17984 |
18288 |
|
6468 |
14244 |
5724 |
8520 |
73 |
46,831,093,727 |
1 |
22 |
2300 | |
20878 |
20878 |
20920 |
21240 |
|
7084 |
15826 |
6304 |
9522 |
73 |
59,405,399,386 |
1 |
23 |
2600 | |
24116 |
24116 |
24160 |
24496 |
|
7728 |
17492 |
6912 |
10580 |
73 |
74,900,592,545 |
1 |
24 |
2925 | |
27673 |
27673 |
27719 |
28071 |
|
8400 |
19242 |
7548 |
11694 |
73 |
94,784,185,716 |
1 |
25 |
3276 | |
31564 |
31564 |
31612 |
31980 |
|
9100 |
21076 |
8212 |
12864 |
73 |
118,150,013,118 |
1 |
26 |
3654 | |
35804 |
35804 |
35854 |
36238 |
|
9828 |
22994 |
8904 |
14090 |
73 |
145,507,204,784 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
112 |
32 |
22 |
10 |
61 |
58,470 |
2 |
3 |
20 | |
12 |
20 |
20 |
24 |
|
252 |
88 |
68 |
20 |
47 |
869,494 |
2 |
4 |
35 | |
9 |
35 |
35 |
51 |
|
448 |
191 |
156 |
35 |
43 |
5,053,284 |
2 |
5 |
56 | |
12 |
56 |
56 |
96 |
|
700 |
356 |
300 |
56 |
43 |
23,598,133 |
2 |
6 |
84 | |
36 |
84 |
98 |
170 |
|
1008 |
598 |
514 |
84 |
49 |
86,342,689 |
2 |
7 |
120 | |
96 |
132 |
176 |
284 |
|
1372 |
932 |
800 |
132 |
62 |
261,091,847 |
2 |
8 |
165 | |
207 |
243 |
305 |
449 |
|
1792 |
1373 |
1130 |
243 |
73 |
647,991,985 |
2 |
9 |
220 | |
384 |
420 |
500 |
680 |
|
2268 |
1932 |
1516 |
416 |
54 |
1,421,437,653 |
2 |
10 |
286 | |
642 |
678 |
776 |
992 |
|
2800 |
2620 |
1958 |
662 |
49 |
2,979,713,435 |
2 |
11 |
364 | |
996 |
1032 |
1148 |
1400 |
|
3388 |
3448 |
2456 |
992 |
39 |
5,638,239,549 |
2 |
12 |
455 | |
1461 |
1497 |
1631 |
1919 |
|
4032 |
4416 |
3010 |
1406 |
36 |
10,146,693,067 |
2 |
13 |
560 | |
2052 |
2088 |
2240 |
2564 |
|
4732 |
5524 |
3620 |
1904 |
34 |
17,266,117,379 |
2 |
14 |
680 | |
2784 |
2820 |
2990 |
3350 |
|
5488 |
6772 |
4286 |
2486 |
32 |
29,030,871,527 |
2 |
15 |
816 | |
3672 |
3708 |
3896 |
4292 |
|
6300 |
8160 |
5008 |
3152 |
31 |
45,388,997,928 |
2 |
16 |
969 | |
4731 |
4767 |
4973 |
5405 |
|
7168 |
9688 |
5786 |
3902 |
30 |
69,822,613,749 |
2 |
17 |
1140 | |
5976 |
6012 |
6236 |
6704 |
|
8092 |
11356 |
6620 |
4736 |
29 |
102,770,434,105 |
2 |
18 |
1330 | |
7422 |
7458 |
7700 |
8204 |
|
9072 |
13164 |
7510 |
5654 |
28 |
148,798,237,838 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
280 |
88 |
68 |
20 |
47 |
897,882 |
3 |
4 |
35 | |
21 |
35 |
35 |
39 |
|
532 |
191 |
156 |
35 |
43 |
7,222,215 |
3 |
5 |
56 | |
12 |
56 |
56 |
72 |
|
868 |
356 |
300 |
56 |
43 |
34,797,001 |
3 |
6 |
84 | |
-4 |
84 |
84 |
124 |
|
1288 |
598 |
514 |
84 |
49 |
133,193,181 |
3 |
7 |
120 | |
-12 |
120 |
120 |
200 |
|
1792 |
932 |
812 |
120 |
54 |
427,858,333 |
3 |
8 |
165 | |
3 |
165 |
179 |
311 |
|
2380 |
1373 |
1208 |
165 |
60 |
1,175,466,417 |
3 |
9 |
220 | |
56 |
220 |
276 |
468 |
|
3052 |
1936 |
1716 |
220 |
68 |
2,837,250,153 |
3 |
10 |
286 | |
162 |
332 |
426 |
682 |
|
3808 |
2636 |
2304 |
332 |
83 |
6,165,419,015 |
3 |
11 |
364 | |
336 |
524 |
644 |
964 |
|
4648 |
3488 |
2964 |
524 |
89 |
12,320,534,739 |
3 |
12 |
455 | |
593 |
799 |
945 |
1329 |
|
5572 |
4503 |
3708 |
795 |
92 |
22,864,928,286 |
3 |
13 |
560 | |
948 |
1172 |
1344 |
1792 |
|
6580 |
5692 |
4536 |
1156 |
94 |
40,375,756,882 |
3 |
14 |
680 | |
1416 |
1658 |
1856 |
2368 |
|
7672 |
7066 |
5448 |
1618 |
96 |
67,777,262,452 |
3 |
15 |
816 | |
2012 |
2272 |
2496 |
3072 |
|
8848 |
8636 |
6444 |
2192 |
97 |
108,338,708,312 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
560 |
191 |
156 |
35 |
43 |
8,140,205 |
4 |
5 |
56 | |
36 |
56 |
56 |
60 |
|
952 |
356 |
300 |
56 |
43 |
42,796,090 |
4 |
6 |
84 | |
22 |
84 |
84 |
100 |
|
1456 |
598 |
514 |
84 |
49 |
173,941,107 |
4 |
7 |
120 | |
-8 |
120 |
120 |
160 |
|
2072 |
932 |
812 |
120 |
54 |
568,508,559 |
4 |
8 |
165 | |
-43 |
165 |
165 |
245 |
|
2800 |
1373 |
1208 |
165 |
60 |
1,628,392,884 |
4 |
9 |
220 | |
-68 |
220 |
220 |
360 |
|
3640 |
1936 |
1716 |
220 |
68 |
4,088,170,401 |
4 |
10 |
286 | |
-68 |
286 |
300 |
516 |
|
4592 |
2636 |
2350 |
286 |
76 |
9,467,543,532 |
4 |
11 |
364 | |
-28 |
364 |
420 |
724 |
|
5656 |
3488 |
3124 |
364 |
70 |
19,904,172,149 |
4 |
12 |
455 | |
67 |
455 |
595 |
995 |
|
6832 |
4507 |
4052 |
455 |
64 |
39,486,354,708 |
4 |
13 |
560 | |
232 |
640 |
840 |
1340 |
|
8120 |
5708 |
5068 |
640 |
78 |
73,435,246,952 |
4 |
14 |
680 | |
482 |
926 |
1170 |
1770 |
|
9520 |
7106 |
6180 |
926 |
87 |
129,440,243,374 |
4 |
15 |
816 | |
832 |
1312 |
1600 |
2300 |
|
11032 |
8712 |
7404 |
1308 |
78 |
217,903,672,925 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
980 |
356 |
300 |
56 |
43 |
47,831,832 |
5 |
6 |
84 | |
58 |
84 |
84 |
88 |
|
1540 |
598 |
514 |
84 |
49 |
200,272,728 |
5 |
7 |
120 | |
40 |
120 |
120 |
136 |
|
2240 |
932 |
812 |
120 |
54 |
682,677,636 |
5 |
8 |
165 | |
1 |
165 |
165 |
205 |
|
3080 |
1373 |
1208 |
165 |
60 |
1,990,777,259 |
5 |
9 |
220 | |
-56 |
220 |
220 |
300 |
|
4060 |
1936 |
1716 |
220 |
68 |
5,178,745,350 |
5 |
10 |
286 | |
-116 |
286 |
286 |
426 |
|
5180 |
2636 |
2350 |
286 |
76 |
12,358,519,803 |
5 |
11 |
364 | |
-164 |
364 |
364 |
588 |
|
6440 |
3488 |
3124 |
364 |
70 |
26,093,515,630 |
5 |
12 |
455 | |
-185 |
455 |
469 |
797 |
|
7840 |
4507 |
4052 |
455 |
64 |
53,511,329,217 |
5 |
13 |
560 | |
-164 |
560 |
616 |
1064 |
|
9380 |
5708 |
5148 |
560 |
68 |
100,119,378,048 |
5 |
14 |
680 | |
-86 |
680 |
820 |
1400 |
|
11060 |
7106 |
6426 |
680 |
73 |
180,703,194,041 |
5 |
15 |
816 | |
64 |
816 |
1096 |
1816 |
|
12880 |
8716 |
7900 |
816 |
84 |
309,092,716,173 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
1568 |
598 |
514 |
84 |
49 |
213,614,541 |
6 |
7 |
120 | |
88 |
120 |
120 |
124 |
|
2324 |
932 |
812 |
120 |
54 |
748,264,707 |
6 |
8 |
165 | |
67 |
165 |
165 |
181 |
|
3248 |
1373 |
1208 |
165 |
60 |
2,277,390,242 |
6 |
9 |
220 | |
20 |
220 |
220 |
260 |
|
4340 |
1936 |
1716 |
220 |
68 |
6,081,453,918 |
6 |
10 |
286 | |
-54 |
286 |
286 |
366 |
|
5600 |
2636 |
2350 |
286 |
76 |
14,549,692,290 |
6 |
11 |
364 | |
-144 |
364 |
364 |
504 |
|
7028 |
3488 |
3124 |
364 |
70 |
31,859,029,888 |
6 |
12 |
455 | |
-235 |
455 |
455 |
679 |
|
8624 |
4507 |
4052 |
455 |
64 |
64,971,816,330 |
6 |
13 |
560 | |
-312 |
560 |
560 |
896 |
|
10388 |
5708 |
5148 |
560 |
68 |
124,305,578,025 |
6 |
14 |
680 | |
-360 |
680 |
694 |
1166 |
|
12320 |
7106 |
6426 |
680 |
73 |
226,567,735,379 |
6 |
15 |
816 | |
-364 |
816 |
872 |
1500 |
|
14420 |
8716 |
7900 |
816 |
84 |
400,916,421,855 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
2352 |
932 |
812 |
120 |
54 |
790,611,391 |
7 |
8 |
165 | |
127 |
165 |
165 |
169 |
|
3332 |
1373 |
1208 |
165 |
60 |
2,428,227,311 |
7 |
9 |
220 | |
104 |
220 |
220 |
236 |
|
4508 |
1936 |
1716 |
220 |
68 |
6,626,530,737 |
7 |
10 |
286 | |
50 |
286 |
286 |
326 |
|
5880 |
2636 |
2350 |
286 |
76 |
16,310,699,692 |
7 |
11 |
364 | |
-36 |
364 |
364 |
444 |
|
7448 |
3488 |
3124 |
364 |
70 |
36,037,641,568 |
7 |
12 |
455 | |
-151 |
455 |
455 |
595 |
|
9212 |
4507 |
4052 |
455 |
64 |
73,618,704,057 |
7 |
13 |
560 | |
-280 |
560 |
560 |
784 |
|
11172 |
5708 |
5148 |
560 |
68 |
142,109,772,100 |
7 |
14 |
680 | |
-408 |
680 |
680 |
1016 |
|
13328 |
7106 |
6426 |
680 |
73 |
262,852,611,098 |
7 |
15 |
816 | |
-520 |
816 |
816 |
1296 |
|
15680 |
8716 |
7900 |
816 |
84 |
458,479,041,669 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
3360 |
1373 |
1208 |
165 |
60 |
2,498,316,361 |
8 |
9 |
220 | |
176 |
220 |
220 |
224 |
|
4592 |
1936 |
1716 |
220 |
68 |
6,930,890,073 |
8 |
10 |
286 | |
152 |
286 |
286 |
302 |
|
6048 |
2636 |
2350 |
286 |
76 |
17,388,313,237 |
8 |
11 |
364 | |
92 |
364 |
364 |
404 |
|
7728 |
3488 |
3124 |
364 |
70 |
38,862,587,949 |
8 |
12 |
455 | |
-5 |
455 |
455 |
535 |
|
9632 |
4507 |
4052 |
455 |
64 |
79,488,230,895 |
8 |
13 |
560 | |
-140 |
560 |
560 |
700 |
|
11760 |
5708 |
5148 |
560 |
68 |
158,030,015,842 |
8 |
14 |
680 | |
-302 |
680 |
680 |
904 |
|
14112 |
7106 |
6426 |
680 |
73 |
297,945,581,908 |
|
Bounds and Dimensions on the generic Morgan-Scott Split
shelling parameters: a0 = 1 a1 = 4 a2 = 6 a3 = 4
Combinatorics:
15 | tetrahedra |
28 | interior faces |
18 | interior edges |
4 | interior vertices |
| |
4 | boundary faces |
6 | boundary edges |
4 | boundary vertices |
| |
32 | faces total |
24 | edges total |
8 | vertices total |