Description of why there are 10 unique meshes for cables in MC mods.

gistfile1.java

    /**
     * There are 64 possible meshes, as each of the 6 sides can be either connected or not connected. In the following
     * the connected state is treated as a 6 bit value where 0 indicates not connected and 1 indicates connected.
     *
     *   0  1    2  3    4  5
     * (+x -x) (+y -y) (+z -z)
     *
     * To derive all the meshes, we first determine the number combinations of values for each number of bits set from 0
     * to 6.
     *
     * 0 - 1
     * 1 - 6
     * 2 - 15
     * 3 - 20
     * 4 - 15
     * 5 - 6
     * 6 - 1
     *
     * Note that this is the 6th row of Pascal's triangle.
     *
     * 0 bits and 6 bits are trivial. They are the not connected and fully connected states.
     *
     * 00 00 00
     *  +
     *
     * 11 11 11
     * (up)
     *  y -z (north)
     *  |/
     * -+- x (east)
     * /|
     *
     * The next two are also simple. with 1 or 5 bits set we have 6 possibilities each. The rotations are also easy to
     * calculate for these.
     *
     * 10 00 00
     *  +-
     *
     * 01 11 11
     *  |/
     * -+
     * /|
     *
     * The rest are slightly more complicated and will be handled one at a time.
     *
     * 2 has two unique meshes. This is because with only two bits set, we have either one or two axes set. Rotations
     * for one axis is trivial. ??? Not sure for the other. ???
     *
     * 11 00 00
     * -+-
     *
     * This mesh has 3 possible orientations. 1 for each +-axis pair.
     *
     * 10 10 00
     *  |
     *  +-
     *
     * This mesh has 12 possible orientations. 3 for each pair of axes times 4 (2^2) for the combination of +- on the
     * two axes.
     *
     * 3 has two unique meshes. This is because either all axis must have a single bit set, or one axis must have
     * both set and another have 1.
     *
     * 11 01 00
     *  -+-
     *   |
     *
     * This mesh has 12 possible orientations. 3 for each +- axis pair time 4 (2^2) for the combination of +- on the
     * second axis.
     *
     * 10 10 10
     *  |
     *  +-
     * /
     *
     * This mesh has 8 possible orientations. One bit may be set in each axis, thus we may treat it as a 3 bit value
     * with 2^3 states.
     *
     * 4 has two unique meshes. There must be at least one +- axis pair, then there is one unique mesh for another
     * +- axis pair, and another unique mesh for separate axes.
     * 
     * 11 11 00
     *  |
     * -+-
     *  |
     *  
     * This mesh has 3 possible orientations. 11 11 00, 11 00 11, 00 11 11.
     *  
     * 10 11 01
     *  |/
     *  +-
     *  |
     *  
     * This mesh has 12 possible orientations. 3 for each +- axis pair times 4 for each of the +- states for the
     * remaining 2 axes.
     * 
     * We use the lowest numerical value of each unique mesh as the primary mesh of that type. Rotations are currently
     * calculated empirically.
     *
     */