For a better understanding of the two tesseract colorings, let me first indicate the eight cubes inside the flattened tesseract:



For the coloring on the right -- where all blue, green, red, and yellow edges are parallel -- let us look at the following tesseract representation ...


... and make the following identifications: South cube = b, West cube = a, North cube = B, East cube = A, Top cube = D, Bottom cube = d, Inner cube = c, Outer cube = C.

For the coloring on the left -- where the red and blue edges are perpendicular to the green and yellow edges -- let us look at the following tesseract representation ...


... and make the following identifications: South cube = b, West cube = a, North cube = B, East cube = A, Top cube = C, Bottom cube = c, Inner cube = d, Outer cube = D.