TAOCP 7.2.2.1 Exercise 340

Exercise 340. [30] There are 29 pentacubes, conveniently identified with one-letter codes:

Figure: pentacube one-letter codes a through F and j through n

Figure: Solid pentacube shapes o through z shown as axonometric drawings

Pieces $o$ through $z$ are called, not surprisingly, the solid pentominoes or flat pentacubes. a) What are the mirror images of a, b, c, d, e, f, A, B, C, D, E, F, j, k, l, $\ldots$, z? b) In how many ways can the solid pentominoes be packed into an $a \times b \times c$ cuboid? c) What "natural" set of 25 pentacubes is able to fill the $5 \times 5 \times 5$ cube?

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