| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I'm not sure if this problem is in here already or not.
I was interested in finding the tetrahedron with smallest volume
that has integer sides and integer volume. Anyhow, I used the
preceding formulas to do a search and believe that the
smallest such volume is 6.
Here is a list of tetrahedra with small volumes (volume < 25).
(I have not eliminated duplications, except when volume < 10.)
a b c A B C volume
-- -- -- -- -- -- ------
2 3 4 8 8 7 6
2 7 8 4 6 5 6
2 7 8 6 4 4 6
2 4 4 7 6 5 6
3 6 6 4 7 8 9
4 6 8 3 7 6 9
6 8 11 10 4 8 15
8 12 14 7 8 10 15
5 7 8 14 12 8 15
7 10 12 8 5 8 15
4 4 5 8 7 6 15
7 10 12 8 14 8 15
4 6 8 7 5 4 15
5 7 8 6 4 4 15
5 8 12 14 8 7 15
8 8 10 4 11 6 15
8 8 10 12 7 5 15
4 4 5 7 8 6 15
4 10 11 8 6 8 15
4 6 8 8 10 11 15
4 6 7 8 5 4 15
7 8 14 8 12 10 15
5 7 8 10 8 12 15
8 8 10 7 12 14 15
8 8 10 7 12 5 15
7 8 14 12 8 5 15
8 8 10 11 4 6 15
8 8 10 12 7 14 15
8 12 14 8 7 5 15
5 8 12 10 7 8 15
4 6 8 8 14 11 21
8 8 10 7 4 6 21
6 6 9 8 11 12 21
8 8 10 4 7 6 21
8 8 14 4 11 6 21
6 8 12 11 6 9 21
2 8 8 10 11 12 21
2 11 12 8 10 9 21
4 11 14 8 8 6 21
6 8 11 14 4 8 21
6 7 8 10 8 4 21
8 14 15 8 13 8 21
2 8 8 10 12 11 21
8 10 12 11 2 8 21
8 9 11 2 12 10 21
8 8 13 15 8 14 21
6 10 13 7 8 4 21
4 6 8 8 10 7 21
7 8 13 6 10 4 21
6 6 9 11 8 12 21
8 8 14 8 15 13 21
4 6 8 13 7 10 21
2 11 12 10 8 8 21
4 7 10 8 8 6 21
8 8 10 13 6 7 21
8 8 13 8 15 14 21
8 10 12 2 11 9 21
8 8 14 15 8 13 21
8 10 11 12 2 8 21
7 8 13 10 6 8 21
8 8 14 11 4 6 21
8 13 15 8 14 8 21
6 11 12 8 6 9 21
2 8 8 11 10 9 21
8 9 11 10 8 2 21
2 8 8 11 9 10 21
6 10 13 8 7 8 21
8 9 11 6 12 6 21
4 7 10 13 6 8 21
8 8 10 6 13 7 21
8 10 11 9 8 2 21
2 9 10 11 8 8 21
2 9 10 8 12 11 21
6 7 8 8 10 13 21
7 7 10 11 3 8 24
6 7 7 12 7 7 24
3 7 8 7 11 10 24
4 7 9 10 7 9 24
6 7 7 4 7 7 24
7 9 10 9 7 12 24
4 7 9 6 9 7 24
4 7 7 6 7 7 24
4 11 11 6 7 7 24
6 7 7 4 9 9 24
9 9 12 7 7 10 24
7 7 12 9 9 4 24
6 7 11 12 11 7 24
3 7 8 11 7 8 24
7 8 11 3 10 7 24
11 11 12 7 7 6 24
6 9 9 4 7 7 24
5 6 7 5 8 7 24
7 7 12 11 11 6 24
4 7 7 12 7 7 24
9 9 12 7 7 4 24
6 7 11 4 11 7 24
7 7 12 7 7 6 24
7 12 13 14 2 8 24
7 8 11 7 8 3 24
3 10 11 7 8 7 24
7 9 10 7 9 4 24
7 7 12 7 7 4 24
4 7 9 12 9 7 24
7 7 10 3 11 8 24
2 7 8 12 14 13 24
8 12 14 13 2 7 24
5 7 8 5 7 6 24
2 13 14 12 8 7 24
4 7 7 6 11 11 24
7 7 12 9 9 10 24
| T.R | Title | User | Personal Name | Date | Lines |
|---|