Notes: on reading the 3d solutions

Each solution is represented by a 12-bit integer,
written in hexadecimal,
with each bit assigned to represent an edge.

Vertices are numbered as follows...
0: (0,0,0)
1: (1,0,0)
2: (0,1,0)
3: (1,1,0)
4: (0,0,1)
5: (1,0,1)
6: (0,1,1)
7: (1,1,1)

Edges are numbered as follows:
0: v0=0, v1=1
1: v0=0, v1=2
2: v0=0, v1=4
3: v0=1, v1=3
4: v0=1, v1=5
5: v0=2, v1=3
6: v0=2, v1=6
7: v0=3, v1=7
8: v0=4, v1=5
9: v0=4, v1=6
10: v0=5, v1=7
11: v0=6, v1=7

Bit 0 (least significant) represents Edge 0.

Example:
0x013 means we keep edges 0,1, and 4, and discard the rest.
To read this, drop the "0x", which stands for hexadecimal, and write
what's left in binary:
013 is 0000 0001 0011,
which has 1's in positions 0, 1, 4, reading from the right. 
So there are three edges:
(0,1,0)----e1----(0,0,0)----e0----(1,0,0)----e4----(1,0,1)

Remember that in hexadecimal, a through f stand for 10 through 15,
that is, 1010, 1011, 1100, 1101, 1110, 1111.