Visible dice faces

a | b | c | d | a^b^c | d*8 | a^b^c^(d*8) | %7
--+---+---+---+-------+-----+-------------+---
1 | 2 | 3 | 4 |     0 |  32 |          32 | 4
1 | 2 | 3 | 5 |     0 |  40 |          40 | 5
1 | 2 | 3 | 6 |     0 |  48 |          48 | 6
1 | 2 | 4 | 3 |     7 |  24 |          31 | 3
1 | 2 | 4 | 5 |     7 |  40 |          47 | 5
1 | 2 | 4 | 6 |     7 |  48 |          55 | 6
1 | 2 | 5 | 3 |     6 |  24 |          30 | 2
1 | 2 | 5 | 4 |     6 |  32 |          38 | 3
1 | 2 | 5 | 6 |     6 |  48 |          54 | 5
1 | 2 | 6 | 3 |     5 |  24 |          29 | 1
1 | 2 | 6 | 4 |     5 |  32 |          37 | 2
1 | 2 | 6 | 5 |     5 |  40 |          45 | 3
1 | 3 | 4 | 2 |     6 |  16 |          22 | 1
1 | 3 | 4 | 5 |     6 |  40 |          46 | 4
1 | 3 | 4 | 6 |     6 |  48 |          54 | 5
1 | 3 | 5 | 2 |     7 |  16 |          23 | 2
1 | 3 | 5 | 4 |     7 |  32 |          39 | 4
1 | 3 | 5 | 6 |     7 |  48 |          55 | 6
1 | 3 | 6 | 2 |     4 |  16 |          20 | 6
1 | 3 | 6 | 4 |     4 |  32 |          36 | 1
1 | 3 | 6 | 5 |     4 |  40 |          44 | 2
1 | 4 | 5 | 2 |     0 |  16 |          16 | 2
1 | 4 | 5 | 3 |     0 |  24 |          24 | 3
1 | 4 | 5 | 6 |     0 |  48 |          48 | 6
1 | 4 | 6 | 2 |     3 |  16 |          19 | 5
1 | 4 | 6 | 3 |     3 |  24 |          27 | 6
1 | 4 | 6 | 5 |     3 |  40 |          43 | 1
1 | 5 | 6 | 2 |     2 |  16 |          18 | 4
1 | 5 | 6 | 3 |     2 |  24 |          26 | 5
1 | 5 | 6 | 4 |     2 |  32 |          34 | 6
2 | 3 | 4 | 1 |     5 |   8 |          13 | 6
2 | 3 | 4 | 5 |     5 |  40 |          45 | 3
2 | 3 | 4 | 6 |     5 |  48 |          53 | 4
2 | 3 | 5 | 1 |     4 |   8 |          12 | 5
2 | 3 | 5 | 4 |     4 |  32 |          36 | 1
2 | 3 | 5 | 6 |     4 |  48 |          52 | 3
2 | 3 | 6 | 1 |     7 |   8 |          15 | 1
2 | 3 | 6 | 4 |     7 |  32 |          39 | 4
2 | 3 | 6 | 5 |     7 |  40 |          47 | 5
2 | 4 | 5 | 1 |     3 |   8 |          11 | 4
2 | 4 | 5 | 3 |     3 |  24 |          27 | 6
2 | 4 | 5 | 6 |     3 |  48 |          51 | 2
2 | 4 | 6 | 1 |     0 |   8 |           8 | 1
2 | 4 | 6 | 3 |     0 |  24 |          24 | 3
2 | 4 | 6 | 5 |     0 |  40 |          40 | 5
2 | 5 | 6 | 1 |     1 |   8 |           9 | 2
2 | 5 | 6 | 3 |     1 |  24 |          25 | 4
2 | 5 | 6 | 4 |     1 |  32 |          33 | 5
3 | 4 | 5 | 1 |     2 |   8 |          10 | 3
3 | 4 | 5 | 2 |     2 |  16 |          18 | 4
3 | 4 | 5 | 6 |     2 |  48 |          50 | 1
3 | 4 | 6 | 1 |     1 |   8 |           9 | 2
3 | 4 | 6 | 2 |     1 |  16 |          17 | 3
3 | 4 | 6 | 5 |     1 |  40 |          41 | 6
3 | 5 | 6 | 1 |     0 |   8 |           8 | 1
3 | 5 | 6 | 2 |     0 |  16 |          16 | 2
3 | 5 | 6 | 4 |     0 |  32 |          32 | 4
4 | 5 | 6 | 1 |     7 |   8 |          15 | 1
4 | 5 | 6 | 2 |     7 |  16 |          23 | 2
4 | 5 | 6 | 3 |     7 |  24 |          31 | 3