In May 2002 while living in Los Angeles I purchased a Shepherd Cube and a Tartan Cube. I noticed that there was no solution online, so I worked out a simple one for each and put them on a web site.
In July 2009 I combined the two into a simple eBook on the Smashwords publishing platform, the source for most of this post.
Note that there is a good write-up of David Singmaster's notation, and the simple solution I refer to. Here is an illustrated version of it on the Ruwix site.
Shepherd Cube solution
Step 1
A generalized Shepherd's cube is based on a regular 3x3x3 Rubik's cube, except each of the fifty-four cubie faces differs only in orientation. When solved, each of the six cube faces has all nine of its cubie faces with the same orientation. The clearest design is a black arrow on a white field, with the arrow pointing up, down, left or right. A solved cube could be oriented so that just looking straight at it (without the viewpoint shifts associated with standard Singmaster notation) the top face points left, the left face towards you, the front face up, the right face away, the far face down and the bottom face right. Opposite faces point in opposite directions.
Step 2
There are only four different types of edge piece, three of each type. Similar-looking edge pieces can be considered interchangeable, with the one exception described below. Read an edge piece as if it were in the top front position, looking at the top face and then the front face, for example, "left-up". This is equivalent to "down-right", which is how it would appear if you flipped the cube over either physically or mentally. There is no need to list out the different types of edge piece.
Step 3
There are only four different types of corner piece. Similar-looking corner pieces can be considered interchangeable, with no exceptions. The four types are:
- One corner piece, when viewed in the top left front position, that has the top face left, the left face towards, the front face up. Any one of the three arrows will point to another face on the same cubie. If you twist this cubie either clockwise or counterclockwise, it will still look the same, so let's call it a "samie".
- One corner piece, found diametrically opposite on a solved cube, that when viewed in the top left front position has the top face towards, the left face up, the front face left. Any one of the three arrows will point to the same cubie. This is the other "samie".
- Three "matchable" corner pieces, each of which has or could have the up face aligned (either left/right or up/down) with the up center and edge pieces. It might sound complex but visually it's obvious -- either the arrow blends in or it's at right angles and stands out as wrong. No further description of this kind of corner cubie is necessary.
- Three "unmatchable" corner pieces, each of which does not have or could not have the up face aligned (either left/right or up/down) with the up center and edge pieces.
Step 4
I am basing this description on an elementary solution, that I believe is known as the Singmaster 2, i.e. make a cross on the up face; solve three corners correctly on the same up face; flip the cube over and solve three of the edge positions in the middle layer; solve three edge positions on the up layer; solve the two remaining edge positions; put the five remaining corner pieces into the correct positions; solve the orientations of those five corner pieces. But use this solution with the modifications as shown below. You can adapt these modifications to your own favorite way of solving a regular cube.
Step 5
Start with the top face center cubie pointing left; rotate the left face so the center cubie points towards you; the front one up; the right one away; the back one down; the bottom one doesn't matter for now. The reason for always starting with the same orientation is so that if you put the cube down, or look away too long, it is easier to figure out where you are up to in the procedure.
Step 6
Make a cross on the up face, starting with the "left-up" edge position, then "down-right", then "right-down", then "up-right". Then put in three corners correctly, starting with the first "samie". For each of the next two, first select a "matchable" corner cubie, and then make sure to align it correctly as you put it into position. Again, if you always solve the same positions in the same order it is easier to figure out where you are if you get lost.
Step 7
Flip the cube over and solve the three edge positions in the middle layer, reading them the same way as before even though you are solving each in the front right position and not the front top position.
Step 8
Orient the center cubie of the up face correctly, i.e. the opposite way to the down face.
Step 9
Now for the remaining edge pieces. Solve the top front edge position, then the top left edge position, then the top back edge position, in that order. At this point comes that exception mentioned above, where similar-looking edge pieces are not necessarily interchangeable. There are two possibilities at this point: situation one, the two remaining edge pieces are already correct or just need to be flipped in place with the regular BU'B'UR'URU'; or situation two, they aren't. With situation two, you need to interchange one of the remaining edge pieces with one or the other of its similar-looking fellows. One swap will work, i.e. transform into situation one, the other won't. So if the first swap doesn't work, the second swap will.
Step 10
Now all the edge pieces are in place and there are at most five corners left to do, with the down right back position being (usually) unsolved. Locate the (usually) unsolved "samie" cubie and put it in the correct position, taking care not to move it afterwards. Rotate the up face so a mismatched cubie is in the up left front position, and put it into a position where it matches. Repeat until all five corner cubies are in correct positions.
Step 11
Do the usual clockwise/counterclockwise twists to solve the corners. There is only one difference you will frequently run into -- everything appears solved except for one corner, which needs to be twisted clockwise or counterclockwise. Use a "samie" as the other cubie of the pair and twist as normal.
