有多少种选法？

王守恩

nyy 发表于 2023-5-23 09:06
四个顶点，4的阶乘=24，最多24，除以2，得到镜像=24/2=12，
不接受反驳！

尊敬的nyy网友！四面体是你的强项。

四面体的6条边是正整数，体积=39，你能来一组解吗？谢谢！

王守恩

谢谢 northwolves！谢谢宝贵的资料！舍不下！

1个四面体的6条边与体积都是正整数，体积一定是3的倍数：0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,......

体积=0可以有无数组解？
体积=3可以有无数组解？
体积=6可以有无数组解？
体积=9可以有无数组解？
......
体积=39,第1组解都那么难找,能说有无数组解？

lihpb00

nyy 发表于 2023-5-23 09:06
四个顶点，4的阶乘=24，最多24，除以2，得到镜像=24/2=12，
不接受反驳！

我也觉得是这个

王守恩

按照A126766: 76, 7, 8, 16, 8, 16, 10, 7, 40, 11, 27, 12, 308, 13, 84, ...

体积=00, {a,b,c,A,B,C}={02,03,04,02,04,04}, 最长边=4
体积=03, {a,b,c,A,B,C}={21,32,47,58,76,56}, 最长边=76
体积=06, {a,b,c,A,B,C}={02,04,04,07,06,05}, 最长边=7
体积=09, {a,b,c,A,B,C}={03,06,06,04,07,08}, 最长边=8
体积=12, {a,b,c,A,B,C}={02,05,06,16,14,13}, 最长边=16
体积=15, {a,b,c,A,B,C}={04,04,05,07,08,06}, 最长边=8
体积=18, {a,b,c,A,B,C}={07,09,11,07,16,11}, 最长边=16
体积=21, {a,b,c,A,B,C}={04,06,08,08,10,07}, 最长边=10
体积=24, {a,b,c,A,B,C}={04,07,07,06,07,07}, 最长边=7
体积=27, {a,b,c,A,B,C}={02,03,04,38,40,40}, 最长边=40
体积=30, {a,b,c,A,B,C}={04,06,07,11,08,08}, 最长边=11
体积=33, {a,b,c,A,B,C}={06,08,08,27,20,25}, 最长边=27
体积=36, {a,b,c,A,B,C}={04,06,07,12,10,12}, 最长边=12
体积=39,    ?                                                 最长边=308?

1,体积=00,还是应该有的。
2,体积=00, 会有无数个答案吗？
3,体积=03, 会有无数个答案吗？
4,体积=06, 会有无数个答案吗？
......
体积=39,第1个答案都那么难找,能说有无数个答案吗？
......

王守恩

我们把体积=00的单独列出来，记最长边=a，看看有什么规律。
为防止出现重复,我们取{a,b,c,A,B,C}大数尽量靠前的，
譬如: a是最大的，且a≥b≥c，b≥B,b≥C, 譬如：
a=1,
a=2,
a=3,
a=4, {a,b,c,A,B,C}={04,04,02,04,03,02},
a=5,
a=6,
a=7, {a,b,c,A,B,C}={07,06,05,02,05,04}={07,04,04,02,03,04},
a=8, {a,b,c,A,B,C}={08,08,08,07,05,03}={08,07,05,02,03,07},
a=9, {a,b,c,A,B,C}={09,09,06,09,05,06},
......
OEIS有这串数吗？可以有好的"按钮"吗?谢谢！

王守恩

真诚请教。
1个四面体, 体积=0, 6条边都是正整数, 记最长边=a，
a(1)=0,
a(2)=0,
a(3)=0,
a(4)=1, {a,b,c,A,B,C}={04,04,02,04,03,02},
a(5)=0,
a(6)=0,
a(7)=2, {a,b,c,A,B,C}={07,06,05,02,05,04}={07,04,04,02,03,04},
a(8)=2, {a,b,c,A,B,C}={08,08,08,07,05,03}={08,07,05,02,03,07},
a(9)=1, {a,b,c,A,B,C}={09,09,06,09,05,06},
......
OEIS会有这串数吗？
可有好的"按钮"来进行搜索?
谢谢各位大侠！谢谢！

说明:
把四面体看作一个平放在桌面上的三角形ABC, P是顶点,
记6条棱BC=a,CA=b,AB=c,Pa=A,PB=B,PC=C,
为防止出现重复,我们取{a,b,c,A,B,C}大数尽量靠前，譬如: a是最大的，且a≥b≥c，b≥B,b≥C,
我真不知道这个算式应该怎样编排(一直不得法),  谢谢各位！

王守恩

接36#。
{{7,4,4,2,3,4},{7,4,4,2,4,3},{7,5,4,2,6,5},{7,5,4,7,5,6},{7,6,5,2,5,4},{7,6,5,7,4,5},{8,7,3,2,5,7},{8,7,3,3,3,5},{8,7,3,5,7,3},{8,7,3,5,8,8},{8,7,3,7,5,7},{8,7,3,8,7,5},{8,6,4,2,4,8},{8,6,4,3,2,6},{8,6,4,3,7,6},{8,6,4,7,4,8},{8,6,4,8,6,7},{8,6,4,8,8,4},{8,8,4,2,4,6},{8,8,4,4,2,6},{8,8,4,4,7,6},{8,8,4,6,8,4},{8,8,4,7,4,6},{8,8,4,8,6,4},{8,5,5,3,4,4},{8,5,5,6,5,5},{8,7,5,2,3,7},{8,7,5,3,7,5},{8,7,5,3,8,8},{8,7,5,5,5,3},{8,7,5,7,3,7},{8,7,5,8,7,3},{8,7,6,3,6,4},{8,7,6,4,8,4},{8,7,6,8,4,6},{8,8,8,3,5,7},{8,8,8,3,7,5},{8,8,8,5,3,7},{8,8,8,5,7,3},{8,8,8,7,3,5},{8,8,8,7,5,3},{9,8,3,1,3,9},{9,8,3,9,9,3},{9,9,3,1,3,8},{9,9,3,3,1,8},{9,9,3,8,9,3},{9,9,3,9,8,3},{9,7,4,3,3,6},{9,7,4,4,8,7},{9,7,4,7,7,4},{9,7,4,9,7,8},{9,6,5,4,9,6},{9,6,5,9,6,9},{9,7,5,1,5,8},{9,7,5,9,8,5},{9,8,5,1,5,7},{9,8,5,9,7,5},{9,6,6,4,4,5},{9,6,6,4,5,4},{9,9,6,4,6,5},{9,9,6,5,9,6},{9,9,6,6,4,5},{9,9,6,9,5,6},{9,8,7,4,7,4},{9,8,7,6,3,6},{9,8,7,9,4,7},{10,8,3,2,2,8},{10,8,4,2,5,6},{10,8,4,5,9,8},{10,8,4,10,8,9},{10,6,5,2,4,8},{10,8,6,5,5,5},{10,8,6,10,8,6},{10,7,7,5,4,6},{10,7,7,5,6,4},{10,8,7,6,2,8},{10,9,8,5,8,4},{10,9,8,10,4,8},{11,10,3,4,7,10},{11,10,3,7,10,11},{11,10,3,11,10,7},{11,9,4,6,10,9},{11,9,4,11,9,10},{11,9,5,3,8,9},{11,9,5,11,9,8},{11,7,6,7,7,6},{11,7,7,5,3,8},{11,7,7,5,8,3},{11,8,7,1,7,9},{11,8,7,11,9,7},{11,9,7,1,7,8},{11,9,7,11,8,7},{11,10,7,3,10,11},{11,10,7,4,3,10},{11,10,7,11,10,3},{11,8,8,6,4,7},{11,8,8,6,7,4},{11,9,8,3,5,9},{11,9,8,11,9,5},{11,10,9,6,9,4},{11,10,9,11,4,9},{11,11,10,3,7,10},{11,11,10,7,3,10},{12,11,2,6,8,10},{12,12,3,8,10,8},{12,12,3,10,8,8},{12,10,4,4,5,7},{12,10,4,7,10,4},{12,10,4,7,11,10},{12,10,4,12,10,11},{12,8,5,4,9,6},{12,8,5,7,12,6},{12,11,5,5,4,8},{12,11,5,8,11,5},{12,8,6,4,3,9},{12,9,6,3,6,12},{12,9,6,4,8,5},{12,9,6,12,12,6},{12,10,6,5,3,9},{12,12,6,3,6,9},{12,12,6,6,3,9},{12,12,6,7,8,5},{12,12,6,8,7,5},{12,12,6,9,12,6},{12,12,6,12,9,6},{12,9,7,2,9,9},{12,9,7,12,9,9},{12,11,7,6,11,7},{12,11,7,7,6,6},{12,8,8,2,8,10},{12,8,8,2,10,8},{12,8,8,10,3,12},{12,8,8,10,12,3},{12,8,8,12,8,10},{12,8,8,12,10,8},{12,10,8,2,8,8},{12,10,8,3,10,8},{12,10,8,6,2,11},{12,10,8,8,9,3},{12,10,8,8,12,3},{12,10,8,12,8,8},{12,9,9,2,7,9},{12,9,9,2,9,7},{12,9,9,7,4,8},{12,9,9,7,8,4},{12,9,9,12,7,9},{12,9,9,12,9,7},{12,11,9,8,3,9},{12,10,10,8,6,6},{12,11,10,7,10,4},{12,11,10,12,4,10}}

northwolves

王守恩 发表于 2023-8-28 11:52
按照A126766: 76, 7, 8, 16, 8, 16, 10, 7, 40, 11, 27, 12, 308, 13, 84, ...

体积=00, {a,b,c,A,B,C}={0 ...

mathe版主找到的两组解

体积=39, {a,b,c,A,B,C}={308,224,85,48,127,194}, 最长边=308
体积=39, {a,b,c,A,B,C}={308,230,91,48,121,188}, 最长边=308

mathe

vol2.zip (7.14 KB, 下载次数: 4)

2023-10-6 16:25 上传

点击文件名下载附件

最长边搜索到不超过482的结果，每个出现的体积最会提供一个例子（体积不超过2000）
另外写程序验证了最长边不超过1600时，体积无法是3*29, 最长边不超过1200时，体积无法是3*41

王守恩

mathe 发表于 2023-10-6 16:26
最长边搜索到不超过482的结果，每个出现的体积最会提供一个例子（体积不超过2000）
另外写程序验证了最长 ...

谢谢 mathe！ 真诚请教。
1个四面体, 体积=0, 6条边都是正整数, 记最长边=a，
a(1)=0,
a(2)=0,
a(3)=0,
a(4)=1, {a,b,c,A,B,C}={04,04,02,04,03,02},
a(5)=0,
a(6)=0,
a(7)=2, {a,b,c,A,B,C}={07,06,05,02,05,04}={07,04,04,02,03,04},
a(8)=2, {a,b,c,A,B,C}={08,08,08,07,05,03}={08,07,05,02,03,07},
a(9)=1, {a,b,c,A,B,C}={09,09,06,09,05,06},
......
OEIS会有这串数吗？我只要这串数：0,0,0,1,0,0,2,2,1,....。
我真不知道这个算式应该怎样编排(一直不得法),  谢谢各位！真诚请教。