Naming the Hexacube pieces — Page 4 of  5

Group 3 — cross-section of 4 units
This group's cross-section is 4 cubes, forming the familiar shapes used in the computer-game Tetris. The 4-unit core has a domino-size (1x1x2) block attached top or bottom on all possible unit cube faces and in 4 possible horizontal orientations — up, down, left, right. In a few cases the domino stands vertically.

Where the addition of a domino makes a piece fit into more than one shape by cross-section, we've given first priority to the 2x2 and secondarily to the T (shown on page 5). Of the remaining dual possibilities, we selected the shapes that added a domino rather than two separated cubes. Where it was unavoidable for cubes to be on both top and bottom simultaneously — in this case, N or S — we gave them all to the N family.

A few pieces are their own, and thus their reverse's, mirror image, such as piece S2d. This piece could as well have been N2d, but since the S family had already been short-changed on the split-cube shapes, we gave the congruent piece to S. Hence there is no N2d piece.

The names of the pieces in this group combine the tetromino name, the number of the covered unit square, and the direction of the domino as u, d, l, r, or v. In those cases where two separate cubes are attached, the names include the numbers of both unit squares, and if one of the cubelets is on the back, its number is preceded by a b.

The drawing shows the numbering key of the cube faces, front and back, and the attached domino as a smaller rectangle in its respective positions. Where there are cubelets simultaneously on top and bottom, a white square denotes a cubelet on top; a black square means the cubelet is on the bottom. The 3-D views show each piece from an angle so all 6 cubes are identifiable.

The 53 pieces of this group are on two pages. Click on the "Continue" button at the bottom to see the next page.

The tetromino-based hexacubes

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