logo
Octamatch   Index  |  Home  |  Send Your Feedback


This page shows possible placements of the solids with squares on two opposite corners and the rest diamonds.
There are 22 possible placements of the solids for squares in upper right/lower left.
There are 21 possible placements of the solids for squares in upper left/lower right.
Five of them show up on both lists:
0,2,15       0,2,21       1,3,22       1,9,22       1,14,21      

One interesting position is 0,6,24, with all solids on one diagonal. All 4 solutions have the same degree of symmetry. This table shows how many solutions exist for each position of the solids, the maximum degree of symmetry (out of 60), and how many of the solutions have the highest symmetry.
The total number of solutions is 2552.
(Where the solids are diagonally symmetric (D), each basic solution is found twice; where the solids are horizontally or vertically symmetric (H or V), solutions are found for each set or corners.)
Squares Upper Right / Lower Left
0,2,1544: 1 of 68 1,3,1645: 4 of 130
0,2,2144: 2 of 48 1,3,2152: 2 of 172
0,3,15 D49: 2 of 42 / 2 1,3,22 H44: 7 of 127
0,3,1643: 1 of 171 1,8,1542: 1 of 163
0,3,2143: 3 of 40 1,8,2144: 1 of 140
0,3,2238: 1 of 5 1,9,1037: 1 of 16
0,8,2143: 1 of 167 1,9,1550: 4 of 163
0,9,21 D46: 2 of 44 / 2 1,9,1645: 1 of 141
0,9,2245: 1 of 8 1,9,2144: 6 of 172
1,3,1039: 1 of 21 1,9,2243: 3 of 135
1,3,1544: 2 of 170 1,14,21 V43: 1 of 50
Squares Upper Left / Lower Right
0,2,1542: 1 of 9 1,3,22 H44: 7 of (127)
0,2,1946: 1 of 27 1,8,1844: 2 of 43
0,2,2142: 2 of 10 1,8,19 D46: 2 of 26 / 2
0,2,2346: 1 of 22 1,8,2238: 1 of 5
0,3,637: 2 of 8 1,8,2338: 4 of 23
0,3,2447: 1 of 1 1,9,2245: 2 of 66
0,4,637: 6 of 8 1,14,1638: 1 of 5
0,6,834: 1 of 1 1,14,21 V43: 1 of (50)
0,6,943: 1 of 6 1,16,1846: 1 of 39
0,6,1944: 2 of 102 1,16,19 D46: 2 of 20 / 2
0,6,24 D39: 4 of 8 / 2