The 2x2x2 cube is solved in the corner sub-group, ignoring the (non-existent)
edges. The so-called "Dinman Style" cube (probably meant to be "diamond")
has the corners cut off and everything stretched to make a somewhat distorted
rhombicuboctahedron (the six center facies are square; the corners are now
triangles, and the old edges are rectangles). Solving this involves only
positioning moves - all orientation (twisting) is invisible. Thus these
two cubes involve two "pure" subgroups. Can anyone design (by either cutting,
recoloring, or even inventing new mechanisms) cubes or pseudo-cubes which
only involve edge-type moves, or which only involve twisting, with
positioning ignored?
--- Stan Isaacs
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