Naming the Hexacube pieces — Page 2 of  5

Group 2 — cross-section of 5 cubes
To turn a pentomino (flat pentacube) into a 3-D hexacube, we simply add one unit cube to the top and bottom of any of the 5 unit square faces of the pentomino. If the pentomino is symmetrical, it gets cubes added on only one side. Each square gets a number, from 1 through 5, reading from top to bottom of the way the piece is viewed.

The X pentomino has only two distinct cube placements, and the I pentomino is not in this group at all, because no matter where we attach the cubelet, all six cubes still make a single cross-section. The Z pentomino gets only 3 on each side, because through rotational symmetry two cubes become identical with the ones at the other end of the piece.

The name of a piece is then the pentomino letter plus the number of the covered cube face. For reversible pieces, the back of the piece is designated with its letter plus b, followed by the unit cube number. The numbers back each other up, being the same down through to the other side.

The drawing shows the numbering key of the cube faces and the attached cube as a smaller square in its respective position. The 3-D views show each piece from an angle so all 6 cubes are identifiable. The 72 pieces of this group occupy two pages. Click on the "Continue" button below to advance to the next page.

The pentomino-based hexacubes

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