Bounds and Dimensions on symmetric Worsey-Piper
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 |
|
36 |
15 |
11 |
4 |
72 |
4,535 |
1 |
2 |
10 | |
10 |
16 |
17 |
21 |
|
108 |
65 |
49 |
16 |
44 |
120,913 |
1 |
3 |
20 | |
40 |
52 |
58 |
64 |
|
216 |
175 |
123 |
52 |
22 |
538,619 |
1 |
4 |
35 | |
118 |
136 |
151 |
156 |
|
360 |
369 |
233 |
136 |
13 |
1,947,304 |
1 |
5 |
56 | |
268 |
292 |
320 |
320 |
|
540 |
671 |
379 |
292 |
8 |
5,251,429 |
1 |
6 |
84 | |
514 |
544 |
589 |
580 |
|
756 |
1081 |
561 |
520 |
5 |
11,976,086 |
1 |
7 |
120 | |
880 |
916 |
982 |
960 |
|
1008 |
1599 |
779 |
820 |
4 |
24,075,016 |
1 |
8 |
165 | |
1390 |
1432 |
1523 |
1484 |
|
1296 |
2225 |
1033 |
1192 |
3 |
43,526,851 |
1 |
9 |
220 | |
2068 |
2116 |
2236 |
2176 |
|
1620 |
2959 |
1323 |
1636 |
2 |
73,289,609 |
1 |
10 |
286 | |
2938 |
2992 |
3145 |
3060 |
|
1980 |
3801 |
1649 |
2152 |
2 |
112,609,492 |
1 |
11 |
364 | |
4024 |
4084 |
4274 |
4160 |
|
2376 |
4751 |
2011 |
2740 |
1 |
169,708,171 |
1 |
12 |
455 | |
5350 |
5416 |
5647 |
5500 |
|
2808 |
5809 |
2409 |
3400 |
1 |
250,776,236 |
1 |
13 |
560 | |
6940 |
7012 |
7288 |
7104 |
|
3276 |
6975 |
2843 |
4132 |
1 |
343,101,883 |
1 |
14 |
680 | |
8818 |
8896 |
9221 |
8996 |
|
3780 |
8249 |
3313 |
4936 |
1 |
469,728,817 |
1 |
15 |
816 | |
11008 |
11092 |
11470 |
11200 |
|
4320 |
9631 |
3819 |
5812 |
1 |
640,076,438 |
1 |
16 |
969 | |
13534 |
13624 |
14059 |
13740 |
|
4896 |
11121 |
4361 |
6760 |
1 |
824,951,026 |
1 |
17 |
1140 | |
16420 |
16516 |
17012 |
16640 |
|
5508 |
12719 |
4939 |
7780 |
1 |
1,053,731,776 |
1 |
18 |
1330 | |
19690 |
19792 |
20353 |
19924 |
|
6156 |
14425 |
5553 |
8872 |
0 |
1,337,554,010 |
1 |
19 |
1540 | |
23368 |
23476 |
24106 |
23616 |
|
6840 |
16239 |
6203 |
10036 |
0 |
1,689,063,412 |
1 |
20 |
1771 | |
27478 |
27592 |
28295 |
27740 |
|
7560 |
18161 |
6889 |
11272 |
0 |
2,075,886,793 |
1 |
21 |
2024 | |
32044 |
32164 |
32944 |
32320 |
|
8316 |
20191 |
7611 |
12580 |
0 |
2,543,035,409 |
1 |
22 |
2300 | |
37090 |
37216 |
38077 |
37380 |
|
9108 |
22329 |
8369 |
13960 |
0 |
3,070,250,290 |
1 |
23 |
2600 | |
42640 |
42772 |
43718 |
42944 |
|
9936 |
24575 |
9163 |
15412 |
0 |
3,656,417,875 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
144 |
65 |
55 |
10 |
63 |
145,308 |
2 |
3 |
20 | |
9 |
26 |
27 |
31 |
|
324 |
175 |
149 |
26 |
47 |
1,436,335 |
2 |
4 |
35 | |
21 |
63 |
67 |
79 |
|
576 |
369 |
306 |
63 |
25 |
7,455,179 |
2 |
5 |
56 | |
69 |
137 |
149 |
166 |
|
900 |
671 |
534 |
137 |
22 |
26,926,961 |
2 |
6 |
84 | |
177 |
271 |
297 |
315 |
|
1296 |
1105 |
834 |
271 |
15 |
70,610,913 |
2 |
7 |
120 | |
369 |
489 |
535 |
549 |
|
1764 |
1695 |
1206 |
489 |
11 |
161,402,706 |
2 |
8 |
165 | |
669 |
815 |
887 |
891 |
|
2304 |
2465 |
1650 |
815 |
8 |
305,471,361 |
2 |
9 |
220 | |
1101 |
1273 |
1377 |
1365 |
|
2916 |
3415 |
2166 |
1249 |
6 |
616,352,688 |
2 |
10 |
286 | |
1689 |
1887 |
2029 |
1995 |
|
3600 |
4545 |
2754 |
1791 |
5 |
1,036,017,042 |
2 |
11 |
364 | |
2457 |
2681 |
2867 |
2805 |
|
4356 |
5855 |
3414 |
2441 |
4 |
1,737,139,472 |
2 |
12 |
455 | |
3429 |
3679 |
3915 |
3819 |
|
5184 |
7345 |
4146 |
3199 |
3 |
2,715,374,646 |
2 |
13 |
560 | |
4629 |
4905 |
5197 |
5061 |
|
6084 |
9015 |
4950 |
4065 |
3 |
3,925,084,824 |
2 |
14 |
680 | |
6081 |
6383 |
6737 |
6555 |
|
7056 |
10865 |
5826 |
5039 |
3 |
5,489,942,214 |
2 |
15 |
816 | |
7809 |
8137 |
8559 |
8325 |
|
8100 |
12895 |
6774 |
6121 |
2 |
8,307,571,503 |
2 |
16 |
969 | |
9837 |
10191 |
10687 |
10395 |
|
9216 |
15105 |
7794 |
7311 |
2 |
10,585,213,952 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
360 |
175 |
155 |
20 |
72 |
1,958,505 |
3 |
4 |
35 | |
13 |
41 |
42 |
46 |
|
684 |
369 |
328 |
41 |
59 |
14,555,525 |
3 |
5 |
56 | |
9 |
80 |
84 |
100 |
|
1116 |
671 |
591 |
80 |
61 |
70,794,818 |
3 |
6 |
84 | |
29 |
152 |
162 |
194 |
|
1656 |
1105 |
953 |
152 |
57 |
232,128,630 |
3 |
7 |
120 | |
97 |
272 |
296 |
340 |
|
2304 |
1695 |
1423 |
272 |
54 |
587,754,612 |
3 |
8 |
165 | |
237 |
464 |
510 |
561 |
|
3060 |
2465 |
2001 |
464 |
46 |
1,229,190,449 |
3 |
9 |
220 | |
473 |
752 |
828 |
880 |
|
3924 |
3439 |
2687 |
752 |
39 |
2,380,765,518 |
3 |
10 |
286 | |
829 |
1160 |
1274 |
1320 |
|
4896 |
4641 |
3481 |
1160 |
31 |
4,353,147,918 |
3 |
11 |
364 | |
1329 |
1712 |
1872 |
1904 |
|
5976 |
6095 |
4383 |
1712 |
26 |
7,698,359,358 |
3 |
12 |
455 | |
1997 |
2432 |
2646 |
2656 |
|
7164 |
7801 |
5393 |
2408 |
22 |
12,089,300,578 |
3 |
13 |
560 | |
2857 |
3344 |
3620 |
3600 |
|
8460 |
9759 |
6511 |
3248 |
20 |
19,569,884,609 |
3 |
14 |
680 | |
3933 |
4472 |
4818 |
4760 |
|
9864 |
11969 |
7737 |
4232 |
18 |
27,463,477,326 |
3 |
15 |
816 | |
5249 |
5840 |
6264 |
6160 |
|
11376 |
14431 |
9071 |
5360 |
16 |
40,496,201,963 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
720 |
369 |
334 |
35 |
76 |
17,479,233 |
4 |
5 |
56 | |
23 |
62 |
63 |
67 |
|
1224 |
671 |
609 |
62 |
69 |
90,721,515 |
4 |
6 |
84 | |
4 |
108 |
112 |
128 |
|
1872 |
1105 |
997 |
108 |
68 |
371,032,200 |
4 |
7 |
120 | |
-2 |
184 |
194 |
230 |
|
2664 |
1695 |
1511 |
184 |
66 |
1,199,421,121 |
4 |
8 |
165 | |
28 |
305 |
326 |
385 |
|
3600 |
2465 |
2160 |
305 |
69 |
3,124,441,925 |
4 |
9 |
220 | |
118 |
487 |
528 |
605 |
|
4680 |
3439 |
2952 |
487 |
64 |
6,671,698,563 |
4 |
10 |
286 | |
292 |
753 |
824 |
913 |
|
5904 |
4641 |
3888 |
753 |
60 |
14,684,601,374 |
4 |
11 |
364 | |
574 |
1127 |
1238 |
1332 |
|
7272 |
6095 |
4968 |
1127 |
59 |
26,262,526,065 |
4 |
12 |
455 | |
988 |
1633 |
1794 |
1885 |
|
8784 |
7825 |
6192 |
1633 |
50 |
42,034,984,452 |
4 |
13 |
560 | |
1558 |
2295 |
2516 |
2595 |
|
10440 |
9855 |
7560 |
2295 |
46 |
69,540,558,513 |
4 |
14 |
680 | |
2308 |
3137 |
3428 |
3485 |
|
12240 |
12209 |
9072 |
3137 |
42 |
114,635,351,227 |
4 |
15 |
816 | |
3262 |
4183 |
4554 |
4579 |
|
14184 |
14887 |
10728 |
4159 |
38 |
171,701,147,690 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1260 |
671 |
615 |
56 |
76 |
99,269,982 |
5 |
6 |
84 | |
40 |
90 |
91 |
95 |
|
1980 |
1105 |
1015 |
90 |
80 |
434,788,556 |
5 |
7 |
120 | |
7 |
144 |
148 |
164 |
|
2880 |
1695 |
1551 |
144 |
81 |
1,530,046,273 |
5 |
8 |
165 | |
-23 |
225 |
235 |
275 |
|
3960 |
2465 |
2240 |
225 |
82 |
4,388,663,278 |
5 |
9 |
220 | |
-29 |
348 |
368 |
440 |
|
5220 |
3439 |
3091 |
348 |
82 |
11,131,754,396 |
5 |
10 |
286 | |
13 |
528 |
565 |
671 |
|
6660 |
4641 |
4113 |
528 |
81 |
24,601,756,218 |
5 |
11 |
364 | |
127 |
780 |
846 |
980 |
|
8280 |
6095 |
5315 |
780 |
79 |
45,766,782,029 |
5 |
12 |
455 | |
337 |
1128 |
1235 |
1390 |
|
10080 |
7825 |
6697 |
1128 |
79 |
86,460,506,157 |
5 |
13 |
560 | |
667 |
1596 |
1756 |
1924 |
|
12060 |
9855 |
8259 |
1596 |
75 |
147,565,673,634 |
5 |
14 |
680 | |
1141 |
2208 |
2433 |
2605 |
|
14220 |
12209 |
10001 |
2208 |
68 |
225,401,523,466 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2016 |
1105 |
1021 |
84 |
84 |
474,659,771 |
6 |
7 |
120 | |
65 |
126 |
127 |
131 |
|
2988 |
1695 |
1569 |
126 |
88 |
1,789,484,113 |
6 |
8 |
165 | |
19 |
189 |
193 |
209 |
|
4176 |
2465 |
2276 |
189 |
87 |
5,187,945,759 |
6 |
9 |
220 | |
-34 |
280 |
290 |
330 |
|
5580 |
3439 |
3159 |
280 |
87 |
13,343,085,171 |
6 |
10 |
286 | |
-74 |
410 |
430 |
506 |
|
7200 |
4641 |
4231 |
410 |
89 |
30,627,430,745 |
6 |
11 |
364 | |
-78 |
594 |
629 |
749 |
|
9036 |
6095 |
5501 |
594 |
85 |
64,082,993,551 |
6 |
12 |
455 | |
-22 |
847 |
906 |
1071 |
|
11088 |
7825 |
6978 |
847 |
85 |
124,855,410,638 |
6 |
13 |
560 | |
118 |
1185 |
1281 |
1484 |
|
13356 |
9855 |
8670 |
1185 |
83 |
216,610,376,272 |
6 |
14 |
680 | |
366 |
1631 |
1778 |
2011 |
|
15840 |
12209 |
10578 |
1631 |
80 |
366,103,681,464 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3024 |
1695 |
1575 |
120 |
89 |
1,854,921,136 |
7 |
8 |
165 | |
99 |
171 |
172 |
176 |
|
4284 |
2465 |
2294 |
171 |
91 |
5,873,949,262 |
7 |
9 |
220 | |
41 |
244 |
248 |
264 |
|
5796 |
3439 |
3195 |
244 |
87 |
14,891,128,106 |
7 |
10 |
286 | |
-34 |
346 |
356 |
396 |
|
7560 |
4641 |
4295 |
346 |
84 |
35,442,787,261 |
7 |
11 |
364 | |
-106 |
484 |
504 |
584 |
|
9576 |
6095 |
5611 |
484 |
81 |
72,194,511,469 |
7 |
12 |
455 | |
-154 |
673 |
708 |
840 |
|
11844 |
7825 |
7152 |
673 |
83 |
143,233,106,195 |
7 |
13 |
560 | |
-154 |
928 |
984 |
1176 |
|
14364 |
9855 |
8927 |
928 |
83 |
278,324,955,962 |
7 |
14 |
680 | |
-82 |
1264 |
1352 |
1604 |
|
17136 |
12209 |
10945 |
1264 |
82 |
492,704,558,881 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4320 |
2465 |
2300 |
165 |
91 |
6,106,269,175 |
8 |
9 |
220 | |
143 |
226 |
227 |
231 |
|
5904 |
3439 |
3213 |
226 |
89 |
16,138,221,805 |
8 |
10 |
286 | |
74 |
310 |
314 |
330 |
|
7776 |
4641 |
4331 |
310 |
88 |
38,683,248,263 |
8 |
11 |
364 | |
-22 |
424 |
434 |
474 |
|
9936 |
6095 |
5671 |
424 |
87 |
79,151,899,537 |
8 |
12 |
455 | |
-125 |
575 |
595 |
675 |
|
12384 |
7825 |
7250 |
575 |
85 |
169,946,086,616 |
8 |
13 |
560 | |
-215 |
774 |
809 |
945 |
|
15120 |
9855 |
9081 |
774 |
87 |
333,782,044,567 |
8 |
14 |
680 | |
-269 |
1036 |
1092 |
1296 |
|
18144 |
12209 |
11173 |
1036 |
87 |
597,554,408,553 |
|
Bounds and Dimensions on symmetric Worsey-Piper
shelling parameters: a0 = 1 a1 = 11 a2 = 11 a3 = 1
Combinatorics:
24 | tetrahedra |
36 | interior faces |
14 | interior edges |
1 | interior vertices |
| |
24 | boundary faces |
36 | boundary edges |
14 | boundary vertices |
| |
60 | faces total |
50 | edges total |
15 | vertices total |