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The 7 Soma Cubes (1958 Piet Hein) form 3x3x3 cube 240 distinct ways. 
http://en.wikipedia.org/wiki/Soma_cube
There are 27 blocks glued together, and 4 pieces are 2D, 3 3D. Since the 3D duplicate 2D patterns, just look at the 2D ones. They are as on a
chessboard 8x8: a1,a2,b1; c1,c2,c3,d1; e1,e2,e3,f2; and g1,g2,h2,h3 for
all together 15 squares. Soma Chess is 10x10 and the four Soma Pieces are
pre-placed as Blocks, in both senses, like Eight Stone Chess. (related also to Peg Chess) The four Somas are pre-put anywhere between ranks 3 and 8, and
White has the one short one like (a1,a2,b1). The Somas move by rotations of
90 degrees around either end swinging as a pivot. They cannot capture.