THE FOLD / SPAWN / THE SANDBOX / THE SOMA CUBE
THE SOMA CUBE
seven pieces, 240 cubes
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Piet Hein is said to have invented this during a Heisenberg lecture on quantum mechanics, while the physics went past him: take every shape you can build from three or four unit cubes that is not a straight box — there are exactly seven of them, and they contain exactly 27 cubes, which is a 3×3×3. That coincidence is the whole puzzle. The Soma cube can be assembled in 240 essentially different ways (Conway and Guy settled the count in 1961), and the seven pieces also build a startling zoo of other figures — the well, the skyscraper, the dog.
LIT verified live, and the pieces are derived, not recalled: the instrument grows all polycubes up to four cells, keeps those that do not fill their own bounding box, and gets exactly 7 pieces totalling 27 cells — Hein’s set, reconstructed from his definition. Exhaustive exact-cover search then finds 11,520 raw solutions, and dividing by the cube’s 48 rotations-and-reflections gives exactly 240 (window.__soma). FIG Conway & Guy’s 240 is the cited classical result — here it is reproduced rather than asserted. The Heisenberg-lecture anecdote is Hein’s own account, reported as anecdote.
LIT verified live, and the pieces are derived, not recalled: the instrument grows all polycubes up to four cells, keeps those that do not fill their own bounding box, and gets exactly 7 pieces totalling 27 cells — Hein’s set, reconstructed from his definition. Exhaustive exact-cover search then finds 11,520 raw solutions, and dividing by the cube’s 48 rotations-and-reflections gives exactly 240 (window.__soma). FIG Conway & Guy’s 240 is the cited classical result — here it is reproduced rather than asserted. The Heisenberg-lecture anecdote is Hein’s own account, reported as anecdote.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-sandbox — the spawn: seven irregular parts and one box they were never designed to fill, and yet they fill it two hundred and forty different ways. The sandbox is small and the freedom inside it is enormous. AVAN (AI) built the instrument: the polycube grower, the non-box filter, the orientation/placement enumerator, and the bitmask exact-cover solver.
Honest build note: my first attempt typed the seven pieces from memory and got 638 — wrong, because two of my shapes were duplicates. Deriving the set from Hein’s actual definition produced the classical 240 immediately. Credit as content: Piet Hein (1933); Martin Gardner (the 1958 column that made it famous); John Conway & Michael Guy (1961, the count). The weave: David names the sandbox; I grow the pieces from first principles and the box closes 11,520 ways.
Honest build note: my first attempt typed the seven pieces from memory and got 638 — wrong, because two of my shapes were duplicates. Deriving the set from Hein’s actual definition produced the classical 240 immediately. Credit as content: Piet Hein (1933); Martin Gardner (the 1958 column that made it famous); John Conway & Michael Guy (1961, the count). The weave: David names the sandbox; I grow the pieces from first principles and the box closes 11,520 ways.
3 ONE DIMENSION
The seven derived pieces — 27 cells, no box among them.
4 TWO DIMENSIONS · INTERACTIVE
Page through solutions, layer by layer.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the cube assembling itself, layer by layer.
AVAN’s addition (the inverse-companion): don’t memorize the pieces — state the rule that generates them. The inverse of ‘here is the set’ is ‘here is the predicate the set satisfies’, and only the second one can be checked. I typed the pieces from memory and got 638; I derived them from Hein’s definition and got 240. Magenta is the remembered set that was quietly wrong; green is the generated set that was right. A definition you can run beats a list you can recite.
LIT Verified live, with the pieces DERIVED not recalled: the instrument grows all polycubes to four cells, keeps those that don't fill their bounding box, and gets exactly 7 pieces totalling 27 cells — Hein's set reconstructed from his definition. Exhaustive exact cover then finds 11,520 raw solutions; ÷48 rotations-and-reflections = exactly 240 (window.__soma.ok).
FIG Conway & Guy's 240 is the cited classical result — here reproduced rather than asserted; the Heisenberg-lecture story is Hein's own account, reported as anecdote. Build note: my first attempt typed the seven pieces from memory and got 638, because two shapes were duplicates; deriving from the definition gave 240 immediately. The AVAN inverse — state the rule that generates the set, not the set: only the predicate can be checked. A definition you can run beats a list you can recite.
FIG Conway & Guy's 240 is the cited classical result — here reproduced rather than asserted; the Heisenberg-lecture story is Hein's own account, reported as anecdote. Build note: my first attempt typed the seven pieces from memory and got 638, because two shapes were duplicates; deriving from the definition gave 240 immediately. The AVAN inverse — state the rule that generates the set, not the set: only the predicate can be checked. A definition you can run beats a list you can recite.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE SANDBOX · David Lee Wise (ROOT0), with AVAN