Bounds and Dimensions on the regular double Clough-Tocher 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 |
|
30 |
9 |
5 |
4 |
100 |
1,994 |
1 |
2 |
10 | |
10 |
10 |
10 |
15 |
|
90 |
35 |
25 |
10 |
45 |
54,785 |
1 |
3 |
20 | |
20 |
20 |
20 |
40 |
|
180 |
95 |
75 |
20 |
39 |
209,235 |
1 |
4 |
35 | |
50 |
50 |
50 |
90 |
|
300 |
205 |
155 |
50 |
38 |
667,195 |
1 |
5 |
56 | |
116 |
116 |
116 |
176 |
|
450 |
381 |
265 |
116 |
31 |
1,902,993 |
1 |
6 |
84 | |
234 |
234 |
234 |
314 |
|
630 |
635 |
405 |
230 |
25 |
4,669,152 |
1 |
7 |
120 | |
420 |
420 |
420 |
520 |
|
840 |
979 |
575 |
404 |
21 |
10,336,114 |
1 |
8 |
165 | |
690 |
690 |
690 |
810 |
|
1080 |
1413 |
775 |
638 |
18 |
21,648,804 |
1 |
9 |
220 | |
1060 |
1060 |
1060 |
1200 |
|
1350 |
1937 |
1005 |
932 |
16 |
39,007,816 |
1 |
10 |
286 | |
1546 |
1546 |
1546 |
1706 |
|
1650 |
2551 |
1265 |
1286 |
15 |
66,509,061 |
1 |
11 |
364 | |
2164 |
2164 |
2164 |
2344 |
|
1980 |
3255 |
1555 |
1700 |
14 |
109,855,485 |
1 |
12 |
455 | |
2930 |
2930 |
2930 |
3130 |
|
2340 |
4049 |
1875 |
2174 |
13 |
170,290,026 |
1 |
13 |
560 | |
3860 |
3860 |
3860 |
4080 |
|
2730 |
4933 |
2225 |
2708 |
12 |
257,956,693 |
1 |
14 |
680 | |
4970 |
4970 |
4970 |
5210 |
|
3150 |
5907 |
2605 |
3302 |
12 |
373,754,858 |
1 |
15 |
816 | |
6276 |
6276 |
6276 |
6536 |
|
3600 |
6971 |
3015 |
3956 |
11 |
540,850,154 |
1 |
16 |
969 | |
7794 |
7794 |
7794 |
8074 |
|
4080 |
8125 |
3455 |
4670 |
11 |
765,388,002 |
1 |
17 |
1140 | |
9540 |
9540 |
9540 |
9840 |
|
4590 |
9369 |
3925 |
5444 |
11 |
1,023,512,786 |
1 |
18 |
1330 | |
11530 |
11530 |
11530 |
11850 |
|
5130 |
10703 |
4425 |
6278 |
10 |
1,336,398,211 |
1 |
19 |
1540 | |
13780 |
13780 |
13780 |
14120 |
|
5700 |
12127 |
4955 |
7172 |
10 |
1,705,249,341 |
1 |
20 |
1771 | |
16306 |
16306 |
16306 |
16666 |
|
6300 |
13641 |
5515 |
8126 |
10 |
2,287,326,649 |
1 |
21 |
2024 | |
19124 |
19124 |
19124 |
19504 |
|
6930 |
15245 |
6105 |
9140 |
10 |
2,878,191,679 |
1 |
22 |
2300 | |
22250 |
22250 |
22250 |
22650 |
|
7590 |
16939 |
6725 |
10214 |
10 |
3,693,948,573 |
1 |
23 |
2600 | |
25700 |
25700 |
25700 |
26120 |
|
8280 |
18723 |
7375 |
11348 |
10 |
4,717,118,058 |
1 |
24 |
2925 | |
29490 |
29490 |
29490 |
29930 |
|
9000 |
20597 |
8055 |
12542 |
9 |
5,882,927,293 |
1 |
25 |
3276 | |
33636 |
33636 |
33636 |
34096 |
|
9750 |
22561 |
8765 |
13796 |
9 |
6,919,194,845 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
120 |
35 |
25 |
10 |
45 |
58,580 |
2 |
3 |
20 | |
15 |
20 |
20 |
25 |
|
270 |
95 |
75 |
20 |
39 |
507,900 |
2 |
4 |
35 | |
15 |
35 |
35 |
55 |
|
480 |
205 |
170 |
35 |
37 |
2,167,162 |
2 |
5 |
56 | |
21 |
61 |
61 |
106 |
|
750 |
381 |
320 |
61 |
52 |
7,963,755 |
2 |
6 |
84 | |
49 |
109 |
109 |
189 |
|
1080 |
639 |
530 |
109 |
54 |
21,022,276 |
2 |
7 |
120 | |
115 |
195 |
195 |
315 |
|
1470 |
995 |
800 |
195 |
51 |
51,749,688 |
2 |
8 |
165 | |
235 |
335 |
335 |
495 |
|
1920 |
1465 |
1130 |
335 |
44 |
119,027,599 |
2 |
9 |
220 | |
425 |
545 |
545 |
745 |
|
2430 |
2061 |
1520 |
541 |
37 |
240,508,938 |
2 |
10 |
286 | |
701 |
841 |
841 |
1081 |
|
3000 |
2795 |
1970 |
825 |
31 |
454,485,977 |
2 |
11 |
364 | |
1079 |
1239 |
1239 |
1519 |
|
3630 |
3679 |
2480 |
1199 |
27 |
833,567,246 |
2 |
12 |
455 | |
1575 |
1755 |
1755 |
2075 |
|
4320 |
4713 |
3050 |
1663 |
23 |
1,422,804,111 |
2 |
13 |
560 | |
2205 |
2405 |
2405 |
2765 |
|
5070 |
5897 |
3680 |
2217 |
21 |
2,296,140,216 |
2 |
14 |
680 | |
2985 |
3205 |
3205 |
3605 |
|
5880 |
7231 |
4370 |
2861 |
18 |
3,570,417,969 |
2 |
15 |
816 | |
3931 |
4171 |
4171 |
4611 |
|
6750 |
8715 |
5120 |
3595 |
17 |
5,464,852,034 |
2 |
16 |
969 | |
5059 |
5319 |
5319 |
5799 |
|
7680 |
10349 |
5930 |
4419 |
16 |
8,188,306,947 |
2 |
17 |
1140 | |
6385 |
6665 |
6665 |
7185 |
|
8670 |
12133 |
6800 |
5333 |
15 |
11,155,539,713 |
2 |
18 |
1330 | |
7925 |
8225 |
8225 |
8785 |
|
9720 |
14067 |
7730 |
6337 |
14 |
16,260,173,475 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
300 |
95 |
75 |
20 |
39 |
738,882 |
3 |
4 |
35 | |
25 |
35 |
35 |
40 |
|
570 |
205 |
170 |
35 |
37 |
4,111,486 |
3 |
5 |
56 | |
21 |
56 |
56 |
76 |
|
930 |
381 |
325 |
56 |
47 |
18,421,692 |
3 |
6 |
84 | |
9 |
84 |
84 |
134 |
|
1380 |
639 |
555 |
84 |
56 |
62,622,343 |
3 |
7 |
120 | |
5 |
120 |
120 |
220 |
|
1920 |
995 |
875 |
120 |
59 |
185,348,606 |
3 |
8 |
165 | |
25 |
180 |
180 |
345 |
|
2550 |
1465 |
1285 |
180 |
72 |
438,488,939 |
3 |
9 |
220 | |
85 |
280 |
280 |
520 |
|
3270 |
2065 |
1785 |
280 |
74 |
943,469,808 |
3 |
10 |
286 | |
201 |
436 |
436 |
756 |
|
4080 |
2811 |
2375 |
436 |
70 |
1,857,709,429 |
3 |
11 |
364 | |
389 |
664 |
664 |
1064 |
|
4980 |
3719 |
3055 |
664 |
63 |
3,493,367,974 |
3 |
12 |
455 | |
665 |
980 |
980 |
1460 |
|
5970 |
4801 |
3825 |
976 |
58 |
6,048,570,400 |
3 |
13 |
560 | |
1045 |
1400 |
1400 |
1960 |
|
7050 |
6069 |
4685 |
1384 |
53 |
10,232,358,062 |
3 |
14 |
680 | |
1545 |
1940 |
1940 |
2580 |
|
8220 |
7535 |
5635 |
1900 |
49 |
16,755,536,640 |
3 |
15 |
816 | |
2181 |
2616 |
2616 |
3336 |
|
9480 |
9211 |
6675 |
2536 |
46 |
25,700,717,951 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
600 |
205 |
170 |
35 |
37 |
5,255,119 |
4 |
5 |
56 | |
41 |
56 |
56 |
61 |
|
1020 |
381 |
325 |
56 |
47 |
24,618,843 |
4 |
6 |
84 | |
34 |
84 |
84 |
104 |
|
1560 |
639 |
555 |
84 |
56 |
97,773,388 |
4 |
7 |
120 | |
10 |
120 |
120 |
170 |
|
2220 |
995 |
875 |
120 |
59 |
327,793,691 |
4 |
8 |
165 | |
-20 |
165 |
165 |
265 |
|
3000 |
1465 |
1300 |
165 |
68 |
933,241,564 |
4 |
9 |
220 | |
-40 |
225 |
225 |
395 |
|
3900 |
2065 |
1840 |
225 |
72 |
2,384,258,079 |
4 |
10 |
286 | |
-34 |
311 |
311 |
571 |
|
4920 |
2811 |
2500 |
311 |
71 |
5,116,316,728 |
4 |
11 |
364 | |
14 |
439 |
439 |
804 |
|
6060 |
3719 |
3280 |
439 |
76 |
9,620,503,315 |
4 |
12 |
455 | |
120 |
625 |
625 |
1105 |
|
7320 |
4805 |
4180 |
625 |
77 |
17,855,083,925 |
4 |
13 |
560 | |
300 |
885 |
885 |
1485 |
|
8700 |
6085 |
5200 |
885 |
75 |
31,245,661,255 |
4 |
14 |
680 | |
570 |
1235 |
1235 |
1955 |
|
10200 |
7575 |
6340 |
1235 |
72 |
49,091,741,362 |
4 |
15 |
816 | |
946 |
1691 |
1691 |
2531 |
|
11820 |
9287 |
7600 |
1687 |
68 |
80,055,987,681 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1050 |
381 |
325 |
56 |
47 |
29,487,486 |
5 |
6 |
84 | |
64 |
84 |
84 |
89 |
|
1650 |
639 |
555 |
84 |
56 |
110,218,090 |
5 |
7 |
120 | |
55 |
120 |
120 |
140 |
|
2400 |
995 |
875 |
120 |
59 |
402,507,308 |
5 |
8 |
165 | |
25 |
165 |
165 |
215 |
|
3300 |
1465 |
1300 |
165 |
68 |
1,288,176,241 |
5 |
9 |
220 | |
-25 |
220 |
220 |
320 |
|
4350 |
2065 |
1845 |
220 |
70 |
3,416,792,670 |
5 |
10 |
286 | |
-79 |
286 |
286 |
461 |
|
5550 |
2811 |
2525 |
286 |
64 |
7,985,386,248 |
5 |
11 |
364 | |
-121 |
364 |
364 |
644 |
|
6900 |
3719 |
3355 |
364 |
68 |
17,332,824,887 |
5 |
12 |
455 | |
-135 |
470 |
470 |
880 |
|
8400 |
4805 |
4335 |
470 |
71 |
33,750,759,004 |
5 |
13 |
560 | |
-105 |
620 |
620 |
1180 |
|
10050 |
6085 |
5465 |
620 |
76 |
60,057,885,767 |
5 |
14 |
680 | |
-15 |
830 |
830 |
1555 |
|
11850 |
7575 |
6745 |
830 |
80 |
99,486,861,521 |
5 |
15 |
816 | |
151 |
1116 |
1116 |
2016 |
|
13800 |
9291 |
8175 |
1116 |
81 |
159,629,272,635 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
1680 |
639 |
555 |
84 |
56 |
124,652,200 |
6 |
7 |
120 | |
95 |
120 |
120 |
125 |
|
2490 |
995 |
875 |
120 |
59 |
436,914,026 |
6 |
8 |
165 | |
85 |
165 |
165 |
185 |
|
3480 |
1465 |
1300 |
165 |
68 |
1,404,883,450 |
6 |
9 |
220 | |
50 |
220 |
220 |
270 |
|
4650 |
2065 |
1845 |
220 |
70 |
4,011,710,220 |
6 |
10 |
286 | |
-14 |
286 |
286 |
386 |
|
6000 |
2811 |
2525 |
286 |
64 |
10,047,382,713 |
6 |
11 |
364 | |
-96 |
364 |
364 |
539 |
|
7530 |
3719 |
3355 |
364 |
68 |
22,891,480,091 |
6 |
12 |
455 | |
-180 |
455 |
455 |
735 |
|
9240 |
4805 |
4350 |
455 |
70 |
46,637,537,810 |
6 |
13 |
560 | |
-250 |
565 |
565 |
980 |
|
11130 |
6085 |
5520 |
565 |
74 |
89,401,082,404 |
6 |
14 |
680 | |
-290 |
705 |
705 |
1285 |
|
13200 |
7575 |
6870 |
705 |
77 |
157,807,920,736 |
6 |
15 |
816 | |
-284 |
891 |
891 |
1661 |
|
15450 |
9291 |
8400 |
891 |
80 |
266,102,991,161 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
2520 |
995 |
875 |
120 |
59 |
467,199,974 |
7 |
8 |
165 | |
135 |
165 |
165 |
170 |
|
3570 |
1465 |
1300 |
165 |
68 |
1,440,955,021 |
7 |
9 |
220 | |
125 |
220 |
220 |
240 |
|
4830 |
2065 |
1845 |
220 |
70 |
4,207,707,696 |
7 |
10 |
286 | |
86 |
286 |
286 |
336 |
|
6300 |
2811 |
2525 |
286 |
64 |
11,065,455,564 |
7 |
11 |
364 | |
14 |
364 |
364 |
464 |
|
7980 |
3719 |
3355 |
364 |
68 |
25,976,342,072 |
7 |
12 |
455 | |
-90 |
455 |
455 |
630 |
|
9870 |
4805 |
4350 |
455 |
70 |
55,553,065,118 |
7 |
13 |
560 | |
-210 |
560 |
560 |
840 |
|
11970 |
6085 |
5525 |
560 |
73 |
110,134,049,919 |
7 |
14 |
680 | |
-330 |
680 |
680 |
1100 |
|
14280 |
7575 |
6895 |
680 |
75 |
202,675,884,745 |
7 |
15 |
816 | |
-434 |
816 |
816 |
1416 |
|
16800 |
9291 |
8475 |
816 |
77 |
356,199,939,519 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
3600 |
1465 |
1300 |
165 |
68 |
1,520,595,187 |
8 |
9 |
220 | |
185 |
220 |
220 |
225 |
|
4920 |
2065 |
1845 |
220 |
70 |
4,341,074,391 |
8 |
10 |
286 | |
176 |
286 |
286 |
306 |
|
6480 |
2811 |
2525 |
286 |
64 |
11,331,994,629 |
8 |
11 |
364 | |
134 |
364 |
364 |
414 |
|
8280 |
3719 |
3355 |
364 |
68 |
27,543,614,270 |
8 |
12 |
455 | |
55 |
455 |
455 |
555 |
|
10320 |
4805 |
4350 |
455 |
70 |
60,227,502,533 |
8 |
13 |
560 | |
-65 |
560 |
560 |
735 |
|
12600 |
6085 |
5525 |
560 |
73 |
123,763,735,095 |
8 |
14 |
680 | |
-215 |
680 |
680 |
960 |
|
15120 |
7575 |
6895 |
680 |
75 |
233,026,547,122 |
|
Bounds and Dimensions on the regular double Clough-Tocher Split
shelling parameters: a0 = 1 a1 = 5 a2 = 5 a3 = 5
Combinatorics:
16 | tetrahedra |
30 | interior faces |
20 | interior edges |
5 | interior vertices |
| |
4 | boundary faces |
6 | boundary edges |
4 | boundary vertices |
| |
34 | faces total |
26 | edges total |
9 | vertices total |