Here is the solution for the Tartan Cube I worked out in 2002. The text below comes from that, as put into a simple eBook along with the Shepherd Cube solution in my previous Steemit post.
Note that there is a good write-up of David Singmaster's notation, and his simple solution that I refer to. Here is an illustrated version of it on the Ruwix site.
I don't apologise for using CAPS for emphasis, like in Step 3. Boldface doesn't give enough emphasis here. Usually it doesn't matter that much if the reader misses an emphasis, but here -- like in Step 3 -- it is, er, REALLY important. 馃槉
A Tartan cube, as invented by Dan Hoey, is a regular 3x3x3 Rubik's cube, except that each of the fifty-four cubie faces is divided into quarters, with one of the colors red, green, yellow, blue in each corner. Each of the six faces has these four colors in different positions, with each cubie face on one cube face looking the same. When solved, the cube could be oriented so that each cubie in the top face reads green, yellow, red, blue when reading top left, top right, bottom left, bottom right respectively. The other faces are oriented as in Step 7.
Always begin and continue the same way so that when taking breaks or getting lost it is easy to orient the cube correctly to see where you are up to.
ALWAYS read colors in the same sequence, i.e. top left, top right, bottom left, bottom right. ALWAYS read an edge piece ending with the common edge, like GYRB or GYBR (same piece). ALWAYS read a corner piece ending up with the common corner, like GYRB or YRGB or RGYB (same piece). It doesn't matter which way you are looking at it. For example, if you put a solved cube on the table and look at the up face without moving your head and the center cubie is, say, GYRB, the back up left corner cubie is BRYG; the back up right corner cubie is RGBY, the left up edge cubie is YBGR and so on. This takes a little bit of getting used to, but it is THE key point in solving this cube rapidly.
Edge pieces. In looking for an edge piece, first note EDGE colors, where the colors extend over the edge from one face to the adjacent face. There are two edge pieces with the same edge colors, for example GYRB/GYBR and YGRB/YGBR. Here both edge pieces have red and blue as edge colors. Note that if ONE face matches then it is the correct edge piece. If it is in the correct position then it must also be in the correct orientation.
Take the first possible edge piece with the correct edge color pair (any order) and notice the top pair. If they match the piece you are searching for, then either the face you are looking at is correct or the other face is. You don't need to check the other face as it HAS to be correct -- you only need to check one face once you have determined it is the correct piece. If you have a piece with the correct edge color pair (any order) and the top pair does not match, drop it, wrong piece. Don't bother to check the other face. Example: you are looking for the edge piece to match GYRB. You find one of the two blue/red edges. The top pair is YG so this is the WRONG piece. You want the other one. You don't need to check the second face of the wrong edge piece. It is very quick to scan over the cube noting edge colors only and ignoring the rest.
Corner pieces. First see what the corner color, extending over three faces, is. There are two corner pieces with the color you want. Example: GYRB/YRGB/RGYB and YGRB/RYGB/GRYB. Note that if ONE face matches and the corner piece is in the correct position, then it is the correct corner cubie in the correct orientation. It is very quick to scan over the cube noting extreme corner colors only and ignoring the rest.
The start position is up face center cubie = GYRB.
Orient the front face so that TOP pair of the center cubie = RB, i.e. the BOTTOM pair of the up face. Rotate the whole cube as needed to find the face that allows RB as the top pair of the center cubie (there is only one face that allows this). Going counterclockwise, rotate the remaining three adjacent faces so the top pair of the center cubie face matches the bottom pair of the up face, i.e. GR, YG, BY.
Here I am using the elementary Singmaster 2 solution, 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 pieces in the middle layer; solve three edge pieces in the up layer; solve the two remaining edge pieces; put the five remaining corner pieces in correct positions; solve orientations of those five corner pieces. You can adapt the procedure to your own preferred methods.
Before starting the step of solving the front, left and back edge pieces, orient the up face correctly. Then solve the up front edge position, then the up left edge position, then the up back edge position. At this point, either the two remaining edge pieces will have been solved automatically, or they are simply inverted and can be flipped using BU'B'UR'URU'. There are no other possibilities.
Put the five remaining corner pieces in place by noting corner colors only and ignoring the rest. This is very quick and very simple. Then fix orientations as needed.
Note that with a corner piece in the correct position, if one face of that cubie is correct then all of them are or if one face is wrong then all of them are.
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