Reference

Turning & building shapes

Two ideas run through every puzzle: a shape can be turned without changing, and any build is a stack of flat layers. Back to the lab anytime: Open the shapes lab →

• Turned vs flipped

  A rotation TURNS a shape — you could do it with your hands without ever lifting it into a mirror. A mirror FLIPS left and right, like your reflection: same-looking, but you can never turn a left glove into a right one. In Rotation Station, only the true turn is right.

• The 24 turns

  A solid block shape can be turned into exactly 24 different positions in space (6 faces it can sit on × 4 spins each). A candidate that matches one of those 24 is a rotation; anything else is a mirror or a different shape.

• Floors, bottom-up

  Every 3-D build is a stack of flat floors. The ground floor sits on the ground; each floor above adds blocks on top. Build the ground floor first, then climb — just like real blocks, you can’t place a block in mid-air with nothing under it. In Layer Cake the floor below shows faintly so you can see what you are building on.

• Across, back, up

  Every block sits at three numbers: how far across, how far back, and which floor. In Layer Cake you pick the floor, then tap the across-and-back grid to place or remove a block on it.

• Three views

  An engineer’s drawing shows a solid from the front, the side and above. Three flat drawings can pin down a shape — though sometimes more than one shape casts the same three views. Try it in Three views.

The people behind the ideas

• Roger Shepard and Jacqueline Metzler · 1971

  They showed people pairs of block figures like the two below and asked: the same object, or two different ones? The bigger the turn between the pair, the longer people took to answer, in a straight line, as if they were turning the shape in their heads at a steady speed. A turn in your head takes time, just like a turn in your hands.

  ✓ Checked Checked against: Wikipedia: Mental rotation

• Lord Kelvin · 1893 (published 1894)

  He gave the mirror twin its name. In a lecture he said a shape is “chiral” if its image in a mirror “cannot be brought to coincide with itself”: no turn makes the two match. Your hands are chiral. So is every corkscrew in Rotation Station.

  ✓ Checked Checked against: Wikipedia: Chirality

• Louis Pasteur · 1848

  Looking closely at crystals of a salt called a tartrate, he saw that half of them were right-handed and half left-handed — mirror twins. Each kind turned a beam of light the opposite way; mixed half and half, they cancelled out. Mirror twins can behave differently, even when they are made of the same things.

  ✓ Checked Checked against: Wikipedia: Louis Pasteur

• Piet Hein · 1933

  During a lecture on quantum physics, the Danish puzzle-maker thought up the Soma cube: seven small block shapes that fit together into one 3×3×3 cube. There are 240 different ways to build it, not counting turns and mirror images.

  ✓ Checked Checked against: Wikipedia: Soma cube

Turning shapes in your head is a skill, not a talent — every puzzle you try makes the next one easier. Try a puzzle →