Bounds and Dimensions on a generic Octahedron
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 |
|
12 |
7 |
3 |
4 |
100 |
612 |
1 |
2 |
10 | |
10 |
10 |
10 |
13 |
|
36 |
25 |
15 |
10 |
64 |
13,413 |
1 |
3 |
20 | |
24 |
24 |
24 |
32 |
|
72 |
63 |
39 |
24 |
45 |
62,961 |
1 |
4 |
35 | |
54 |
54 |
54 |
68 |
|
120 |
129 |
75 |
54 |
34 |
244,758 |
1 |
5 |
56 | |
108 |
108 |
108 |
128 |
|
180 |
231 |
123 |
108 |
28 |
781,587 |
1 |
6 |
84 | |
194 |
194 |
194 |
220 |
|
252 |
369 |
183 |
186 |
24 |
2,053,359 |
1 |
7 |
120 | |
320 |
320 |
320 |
352 |
|
336 |
543 |
255 |
288 |
22 |
4,639,341 |
1 |
8 |
165 | |
494 |
494 |
494 |
532 |
|
432 |
753 |
339 |
414 |
21 |
9,360,195 |
1 |
9 |
220 | |
724 |
724 |
724 |
768 |
|
540 |
999 |
435 |
564 |
20 |
17,319,090 |
1 |
10 |
286 | |
1018 |
1018 |
1018 |
1068 |
|
660 |
1281 |
543 |
738 |
20 |
29,942,814 |
1 |
11 |
364 | |
1384 |
1384 |
1384 |
1440 |
|
792 |
1599 |
663 |
936 |
19 |
49,022,886 |
1 |
12 |
455 | |
1830 |
1830 |
1830 |
1892 |
|
936 |
1953 |
795 |
1158 |
19 |
76,756,668 |
1 |
13 |
560 | |
2364 |
2364 |
2364 |
2432 |
|
1092 |
2343 |
939 |
1404 |
18 |
115,788,477 |
1 |
14 |
680 | |
2994 |
2994 |
2994 |
3068 |
|
1260 |
2769 |
1095 |
1674 |
18 |
169,250,697 |
1 |
15 |
816 | |
3728 |
3728 |
3728 |
3808 |
|
1440 |
3231 |
1263 |
1968 |
18 |
240,804,891 |
1 |
16 |
969 | |
4574 |
4574 |
4574 |
4660 |
|
1632 |
3729 |
1443 |
2286 |
18 |
334,682,913 |
1 |
17 |
1140 | |
5540 |
5540 |
5540 |
5632 |
|
1836 |
4263 |
1635 |
2628 |
17 |
455,728,020 |
1 |
18 |
1330 | |
6634 |
6634 |
6634 |
6732 |
|
2052 |
4833 |
1839 |
2994 |
17 |
609,435,984 |
1 |
19 |
1540 | |
7864 |
7864 |
7864 |
7968 |
|
2280 |
5439 |
2055 |
3384 |
17 |
801,996,204 |
1 |
20 |
1771 | |
9238 |
9238 |
9238 |
9348 |
|
2520 |
6081 |
2283 |
3798 |
17 |
1,040,332,818 |
1 |
21 |
2024 | |
10764 |
10764 |
10764 |
10880 |
|
2772 |
6759 |
2523 |
4236 |
17 |
1,332,145,815 |
1 |
22 |
2300 | |
12450 |
12450 |
12450 |
12572 |
|
3036 |
7473 |
2775 |
4698 |
17 |
1,685,952,147 |
1 |
23 |
2600 | |
14304 |
14304 |
14304 |
14432 |
|
3312 |
8223 |
3039 |
5184 |
17 |
2,111,126,841 |
1 |
24 |
2925 | |
16334 |
16334 |
16334 |
16468 |
|
3600 |
9009 |
3315 |
5694 |
17 |
2,617,944,111 |
1 |
25 |
3276 | |
18548 |
18548 |
18548 |
18688 |
|
3900 |
9831 |
3603 |
6228 |
17 |
3,217,618,470 |
1 |
26 |
3654 | |
20954 |
20954 |
20954 |
21100 |
|
4212 |
10689 |
3903 |
6786 |
17 |
3,922,345,842 |
1 |
27 |
4060 | |
23560 |
23560 |
23560 |
23712 |
|
4536 |
11583 |
4215 |
7368 |
16 |
4,745,344,674 |
1 |
28 |
4495 | |
26374 |
26374 |
26374 |
26532 |
|
4872 |
12513 |
4539 |
7974 |
16 |
5,700,897,048 |
1 |
29 |
4960 | |
29404 |
29404 |
29404 |
29568 |
|
5220 |
13479 |
4875 |
8604 |
16 |
6,804,389,793 |
1 |
30 |
5456 | |
32658 |
32658 |
32658 |
32828 |
|
5580 |
14481 |
5223 |
9258 |
16 |
8,072,355,597 |
1 |
31 |
5984 | |
36144 |
36144 |
36144 |
36320 |
|
5952 |
15519 |
5583 |
9936 |
16 |
9,522,514,119 |
1 |
32 |
6545 | |
39870 |
39870 |
39870 |
40052 |
|
6336 |
16593 |
5955 |
10638 |
16 |
11,173,813,101 |
1 |
33 |
7140 | |
43844 |
43844 |
43844 |
44032 |
|
6732 |
17703 |
6339 |
11364 |
16 |
13,046,469,480 |
1 |
34 |
7770 | |
48074 |
48074 |
48074 |
48268 |
|
7140 |
18849 |
6735 |
12114 |
16 |
15,162,010,500 |
1 |
35 |
8436 | |
52568 |
52568 |
52568 |
52768 |
|
7560 |
20031 |
7143 |
12888 |
16 |
17,543,314,824 |
1 |
36 |
9139 | |
57334 |
57334 |
57334 |
57540 |
|
7992 |
21249 |
7563 |
13686 |
16 |
20,214,653,646 |
1 |
37 |
9880 | |
62380 |
62380 |
62380 |
62592 |
|
8436 |
22503 |
7995 |
14508 |
16 |
23,201,731,803 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
48 |
25 |
15 |
10 |
64 |
15,510 |
2 |
3 |
20 | |
17 |
20 |
20 |
23 |
|
108 |
63 |
43 |
20 |
48 |
159,635 |
2 |
4 |
35 | |
29 |
35 |
35 |
47 |
|
192 |
129 |
94 |
35 |
47 |
751,773 |
2 |
5 |
56 | |
53 |
59 |
62 |
86 |
|
300 |
231 |
172 |
59 |
53 |
2,953,718 |
2 |
6 |
84 | |
97 |
103 |
109 |
147 |
|
432 |
377 |
274 |
103 |
42 |
9,279,092 |
2 |
7 |
120 | |
169 |
175 |
184 |
237 |
|
588 |
575 |
400 |
175 |
37 |
25,611,332 |
2 |
8 |
165 | |
277 |
283 |
295 |
363 |
|
768 |
833 |
550 |
283 |
29 |
59,731,147 |
2 |
9 |
220 | |
429 |
435 |
450 |
533 |
|
972 |
1151 |
724 |
427 |
25 |
131,695,184 |
2 |
10 |
286 | |
633 |
639 |
657 |
755 |
|
1200 |
1529 |
922 |
607 |
22 |
263,965,515 |
2 |
11 |
364 | |
897 |
903 |
924 |
1037 |
|
1452 |
1967 |
1144 |
823 |
20 |
497,001,015 |
2 |
12 |
455 | |
1229 |
1235 |
1259 |
1387 |
|
1728 |
2465 |
1390 |
1075 |
19 |
895,822,853 |
2 |
13 |
560 | |
1637 |
1643 |
1670 |
1813 |
|
2028 |
3023 |
1660 |
1363 |
18 |
1,525,728,643 |
2 |
14 |
680 | |
2129 |
2135 |
2165 |
2323 |
|
2352 |
3641 |
1954 |
1687 |
18 |
2,514,473,441 |
2 |
15 |
816 | |
2713 |
2719 |
2752 |
2925 |
|
2700 |
4319 |
2272 |
2047 |
17 |
3,980,992,175 |
2 |
16 |
969 | |
3397 |
3403 |
3439 |
3627 |
|
3072 |
5057 |
2614 |
2443 |
17 |
6,140,958,587 |
2 |
17 |
1140 | |
4189 |
4195 |
4234 |
4437 |
|
3468 |
5855 |
2980 |
2875 |
16 |
9,146,767,786 |
2 |
18 |
1330 | |
5097 |
5103 |
5145 |
5363 |
|
3888 |
6713 |
3370 |
3343 |
16 |
13,318,307,804 |
2 |
19 |
1540 | |
6129 |
6135 |
6180 |
6413 |
|
4332 |
7631 |
3784 |
3847 |
16 |
19,057,420,647 |
2 |
20 |
1771 | |
7293 |
7299 |
7347 |
7595 |
|
4800 |
8609 |
4222 |
4387 |
16 |
26,579,095,488 |
2 |
21 |
2024 | |
8597 |
8603 |
8654 |
8917 |
|
5292 |
9647 |
4684 |
4963 |
15 |
36,662,581,088 |
2 |
22 |
2300 | |
10049 |
10055 |
10109 |
10387 |
|
5808 |
10745 |
5170 |
5575 |
15 |
49,481,508,094 |
2 |
23 |
2600 | |
11657 |
11663 |
11720 |
12013 |
|
6348 |
11903 |
5680 |
6223 |
15 |
66,057,363,608 |
2 |
24 |
2925 | |
13429 |
13435 |
13495 |
13803 |
|
6912 |
13121 |
6214 |
6907 |
15 |
87,081,092,906 |
2 |
25 |
3276 | |
15373 |
15379 |
15442 |
15765 |
|
7500 |
14399 |
6772 |
7627 |
15 |
113,512,241,393 |
2 |
26 |
3654 | |
17497 |
17503 |
17569 |
17907 |
|
8112 |
15737 |
7354 |
8383 |
15 |
146,114,026,933 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
120 |
63 |
43 |
20 |
48 |
180,872 |
3 |
4 |
35 | |
29 |
35 |
35 |
38 |
|
228 |
129 |
94 |
35 |
47 |
1,164,183 |
3 |
5 |
56 | |
41 |
56 |
56 |
68 |
|
372 |
231 |
175 |
56 |
53 |
5,134,289 |
3 |
6 |
84 | |
61 |
84 |
85 |
114 |
|
552 |
377 |
293 |
84 |
64 |
17,691,604 |
3 |
7 |
120 | |
97 |
126 |
130 |
180 |
|
768 |
575 |
449 |
126 |
65 |
51,635,026 |
3 |
8 |
165 | |
157 |
192 |
199 |
273 |
|
1020 |
833 |
641 |
192 |
69 |
129,786,646 |
3 |
9 |
220 | |
249 |
290 |
300 |
400 |
|
1308 |
1159 |
869 |
290 |
70 |
275,288,407 |
3 |
10 |
286 | |
381 |
428 |
441 |
568 |
|
1632 |
1561 |
1133 |
428 |
71 |
556,190,850 |
3 |
11 |
364 | |
561 |
614 |
630 |
784 |
|
1992 |
2047 |
1433 |
614 |
71 |
1,068,262,380 |
3 |
12 |
455 | |
797 |
856 |
875 |
1056 |
|
2388 |
2617 |
1769 |
848 |
77 |
1,924,170,042 |
3 |
13 |
560 | |
1097 |
1162 |
1184 |
1392 |
|
2820 |
3271 |
2141 |
1130 |
61 |
3,305,879,970 |
3 |
14 |
680 | |
1469 |
1540 |
1565 |
1800 |
|
3288 |
4009 |
2549 |
1460 |
52 |
5,476,490,287 |
3 |
15 |
816 | |
1921 |
1998 |
2026 |
2288 |
|
3792 |
4831 |
2993 |
1838 |
46 |
8,786,065,986 |
3 |
16 |
969 | |
2461 |
2544 |
2575 |
2864 |
|
4332 |
5737 |
3473 |
2264 |
43 |
13,439,727,312 |
3 |
17 |
1140 | |
3097 |
3186 |
3220 |
3536 |
|
4908 |
6727 |
3989 |
2738 |
41 |
20,330,592,559 |
3 |
18 |
1330 | |
3837 |
3932 |
3969 |
4312 |
|
5520 |
7801 |
4541 |
3260 |
39 |
29,888,125,674 |
3 |
19 |
1540 | |
4689 |
4790 |
4830 |
5200 |
|
6168 |
8959 |
5129 |
3830 |
38 |
43,301,144,706 |
3 |
20 |
1771 | |
5661 |
5768 |
5811 |
6208 |
|
6852 |
10201 |
5753 |
4448 |
37 |
61,106,803,222 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
240 |
129 |
94 |
35 |
47 |
1,378,215 |
4 |
5 |
56 | |
47 |
56 |
56 |
59 |
|
408 |
231 |
175 |
56 |
53 |
6,668,423 |
4 |
6 |
84 | |
60 |
84 |
84 |
96 |
|
624 |
377 |
293 |
84 |
64 |
24,562,138 |
4 |
7 |
120 | |
78 |
120 |
120 |
150 |
|
888 |
575 |
455 |
120 |
64 |
78,248,924 |
4 |
8 |
165 | |
108 |
165 |
168 |
225 |
|
1200 |
833 |
668 |
165 |
67 |
201,306,743 |
4 |
9 |
220 | |
158 |
227 |
236 |
325 |
|
1560 |
1159 |
932 |
227 |
70 |
471,177,333 |
4 |
10 |
286 | |
236 |
317 |
332 |
457 |
|
1968 |
1561 |
1244 |
317 |
72 |
1,098,005,569 |
4 |
11 |
364 | |
350 |
443 |
464 |
628 |
|
2424 |
2047 |
1604 |
443 |
75 |
2,104,668,463 |
4 |
12 |
455 | |
508 |
613 |
640 |
845 |
|
2928 |
2625 |
2012 |
613 |
58 |
3,973,293,905 |
4 |
13 |
560 | |
718 |
835 |
868 |
1115 |
|
3480 |
3303 |
2468 |
835 |
49 |
6,869,375,320 |
4 |
14 |
680 | |
988 |
1117 |
1156 |
1445 |
|
4080 |
4089 |
2972 |
1117 |
43 |
11,634,824,436 |
4 |
15 |
816 | |
1326 |
1467 |
1512 |
1843 |
|
4728 |
4983 |
3524 |
1459 |
40 |
18,474,369,959 |
4 |
16 |
969 | |
1740 |
1893 |
1944 |
2317 |
|
5424 |
5985 |
4124 |
1861 |
38 |
28,118,182,660 |
4 |
17 |
1140 | |
2238 |
2403 |
2460 |
2875 |
|
6168 |
7095 |
4772 |
2323 |
36 |
42,163,705,117 |
4 |
18 |
1330 | |
2828 |
3005 |
3068 |
3525 |
|
6960 |
8313 |
5468 |
2845 |
36 |
63,338,680,920 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
420 |
231 |
175 |
56 |
53 |
7,280,045 |
5 |
6 |
84 | |
72 |
84 |
84 |
87 |
|
660 |
377 |
293 |
84 |
64 |
29,444,458 |
5 |
7 |
120 | |
87 |
120 |
120 |
132 |
|
960 |
575 |
455 |
120 |
64 |
96,286,739 |
5 |
8 |
165 | |
105 |
165 |
165 |
195 |
|
1320 |
833 |
668 |
165 |
67 |
267,685,916 |
5 |
9 |
220 | |
131 |
220 |
220 |
280 |
|
1740 |
1159 |
939 |
220 |
69 |
680,898,971 |
5 |
10 |
286 | |
173 |
286 |
291 |
391 |
|
2220 |
1561 |
1275 |
286 |
71 |
1,491,466,197 |
5 |
11 |
364 | |
239 |
370 |
386 |
532 |
|
2760 |
2047 |
1677 |
370 |
73 |
3,034,901,993 |
5 |
12 |
455 | |
337 |
486 |
513 |
710 |
|
3360 |
2625 |
2139 |
486 |
74 |
6,002,818,794 |
5 |
13 |
560 | |
475 |
642 |
680 |
932 |
|
4020 |
3303 |
2661 |
642 |
76 |
10,618,871,580 |
5 |
14 |
680 | |
661 |
846 |
895 |
1205 |
|
4740 |
4089 |
3243 |
846 |
78 |
18,302,336,384 |
5 |
15 |
816 | |
903 |
1106 |
1166 |
1536 |
|
5520 |
4991 |
3885 |
1106 |
80 |
30,304,646,790 |
5 |
16 |
969 | |
1209 |
1430 |
1501 |
1932 |
|
6360 |
6017 |
4587 |
1430 |
82 |
48,589,677,151 |
5 |
17 |
1140 | |
1587 |
1826 |
1908 |
2400 |
|
7260 |
7175 |
5349 |
1826 |
83 |
75,374,127,007 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
672 |
377 |
293 |
84 |
64 |
31,531,333 |
6 |
7 |
120 | |
105 |
120 |
120 |
123 |
|
996 |
575 |
455 |
120 |
64 |
109,570,013 |
6 |
8 |
165 | |
123 |
165 |
165 |
177 |
|
1392 |
833 |
668 |
165 |
67 |
322,405,781 |
6 |
9 |
220 | |
142 |
220 |
220 |
250 |
|
1860 |
1159 |
939 |
220 |
69 |
856,433,696 |
6 |
10 |
286 | |
166 |
286 |
286 |
346 |
|
2400 |
1561 |
1275 |
286 |
71 |
1,969,063,392 |
6 |
11 |
364 | |
202 |
364 |
364 |
469 |
|
3012 |
2047 |
1683 |
364 |
72 |
4,217,174,742 |
6 |
12 |
455 | |
258 |
455 |
462 |
623 |
|
3696 |
2625 |
2170 |
455 |
72 |
8,367,839,313 |
6 |
13 |
560 | |
342 |
569 |
588 |
812 |
|
4452 |
3303 |
2734 |
569 |
73 |
15,141,890,549 |
6 |
14 |
680 | |
462 |
719 |
750 |
1043 |
|
5280 |
4089 |
3370 |
719 |
74 |
26,060,470,623 |
6 |
15 |
816 | |
626 |
913 |
956 |
1323 |
|
6180 |
4991 |
4078 |
913 |
75 |
45,102,348,264 |
6 |
16 |
969 | |
842 |
1159 |
1214 |
1659 |
|
7152 |
6017 |
4858 |
1159 |
77 |
71,268,303,820 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
1008 |
575 |
455 |
120 |
64 |
115,030,496 |
7 |
8 |
165 | |
147 |
165 |
165 |
168 |
|
1428 |
833 |
668 |
165 |
67 |
343,971,191 |
7 |
9 |
220 | |
169 |
220 |
220 |
232 |
|
1932 |
1159 |
939 |
220 |
69 |
958,053,617 |
7 |
10 |
286 | |
190 |
286 |
286 |
316 |
|
2520 |
1561 |
1275 |
286 |
71 |
2,273,164,854 |
7 |
11 |
364 | |
214 |
364 |
364 |
424 |
|
3192 |
2047 |
1683 |
364 |
72 |
4,802,428,665 |
7 |
12 |
455 | |
246 |
455 |
455 |
560 |
|
3948 |
2625 |
2170 |
455 |
72 |
9,780,227,658 |
7 |
13 |
560 | |
294 |
560 |
562 |
728 |
|
4788 |
3303 |
2743 |
560 |
72 |
18,582,270,180 |
7 |
14 |
680 | |
366 |
680 |
693 |
932 |
|
5712 |
4089 |
3409 |
680 |
73 |
33,153,799,901 |
7 |
15 |
816 | |
470 |
826 |
856 |
1176 |
|
6720 |
4991 |
4165 |
826 |
74 |
56,192,500,049 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
1440 |
833 |
668 |
165 |
67 |
355,831,562 |
8 |
9 |
220 | |
199 |
220 |
220 |
223 |
|
1968 |
1159 |
939 |
220 |
69 |
1,007,906,603 |
8 |
10 |
286 | |
226 |
286 |
286 |
298 |
|
2592 |
1561 |
1275 |
286 |
71 |
2,439,661,851 |
8 |
11 |
364 | |
250 |
364 |
364 |
394 |
|
3312 |
2047 |
1683 |
364 |
72 |
5,378,970,276 |
8 |
12 |
455 | |
275 |
455 |
455 |
515 |
|
4128 |
2625 |
2170 |
455 |
72 |
10,860,258,768 |
8 |
13 |
560 | |
305 |
560 |
560 |
665 |
|
5040 |
3303 |
2743 |
560 |
72 |
20,709,494,559 |
8 |
14 |
680 | |
347 |
680 |
680 |
848 |
|
6048 |
4089 |
3409 |
680 |
73 |
37,724,574,272 |
8 |
15 |
816 | |
409 |
816 |
820 |
1068 |
|
7152 |
4991 |
4175 |
816 |
74 |
66,420,042,620 |
|
Bounds and Dimensions on a generic Octahedron
shelling parameters: a0 = 1 a1 = 3 a2 = 3 a3 = 1
Combinatorics:
8 | tetrahedra |
12 | interior faces |
6 | interior edges |
1 | interior vertices |
| |
8 | boundary faces |
12 | boundary edges |
6 | boundary vertices |
| |
20 | faces total |
18 | edges total |
7 | vertices total |