Square-1: The Twisty Puzzle That Stops Being a Cube

Quick answer: the Square-1 is a three-layer twisty puzzle invented in 1990 by Karel Hršel and Vojtěch Kopský, originally sold as Back to Square One and later as Cube 21. Its layers are cut into kites and triangles rather than equal cubies, so it changes shape as you turn it. That is the whole point and the whole difficulty.

Best for: solvers who have exhausted the normal cube and want something that stops looking like a puzzle halfway through.

Scramble a Rubik's Cube and you still have a cube. Scramble this and you have an object you would struggle to describe.

Watch: A Square-1 Mod Being Solved

Twenty minutes on a modified Square-1 made by MattStudios, a mod of a puzzle already reckoned among the hardest twisty puzzles there are. Worth watching for how unrecognisable the thing becomes mid-solve.

What Is a Square-1?

Three layers, cut unlike anything else.

The top and bottom layers each hold four kite-shaped corner pieces and four triangular edge pieces. The kites occupy twice the angle the triangles do, which is the fact everything else follows from.

The middle layer is only two trapezoid pieces. Between them they form either a square or an irregular hexagon depending on how they sit, and that single joint is what lets the whole puzzle distort.

The outer layers turn in 180 degree increments and the middle in 90 degree increments. A Czechoslovak patent was filed on 8 November 1990, with a US design patent that December.

Why Does It Change Shape?

Because the pieces are different angular widths, so a layer is not obliged to add up to a circle the same way twice.

On a standard cube every piece occupies the same ninety degrees of its layer, so any turn lands pieces exactly where other pieces were. The shape cannot change because every slot is interchangeable.

Here a kite is twice a triangle. Turn a layer and you can bring a kite to a boundary where a triangle used to sit, and the layer now bulges. Do it repeatedly and the cube becomes a stepped, irregular solid.

That is why a half-solved Square-1 looks broken rather than scrambled, and why people put them down.

What Is a Square-1 Mod?

The puzzle in the video above is not a stock Square-1, and the distinction is worth drawing.

A mod takes an existing mechanism and recuts the outside of it. The internals stay the same, so the mathematics and the legal moves are unchanged, but the visible shape is different, which means every piece of visual recognition you have built up stops working.

Applied to a Square-1 that is a fairly brutal idea, because the stock puzzle is already one where recognising the state is most of the skill. The underlying puzzle was hard to read; the mod makes it harder to read while changing nothing about what you must actually do.

It is also why mods are a genuine subculture rather than a novelty. A modder is not inventing a new mechanism, they are attacking the solver's perception of a known one, which is a different kind of design problem and closer to what the Mirror Cube does to a standard 3x3x3.

Why Is the Square-1 So Hard?

Three reasons, and only one is shared with other twisty puzzles.

You have to restore the shape before you can solve the colours. Most methods begin by getting back to a cube, which is a whole puzzle before the actual puzzle starts.

The turns are not always legal. Pieces must line up across the cut before a layer will move, so a great many positions simply refuse, and recognising which is part of the skill.

Parity. The two middle trapezoids can end in a state that no amount of ordinary sequencing fixes, requiring a dedicated algorithm. As with the 15 puzzle, the puzzle can present you with something that looks one move from done and is not reachable at all.

Is It a Speedcubing Event?

Yes, and that is a useful signal about the puzzle.

Square-1 is an official World Cube Association event, which puts it in a small group of twisty puzzles considered worth competing on. Plenty of shape mods and novelties never get near that, because they turn out to be awkward rather than deep once people study them.

Competitive solvers reach times that look impossible given what the puzzle does mid-solve, and they get there with methods built around exactly the two obstacles above: restore the shape fast, then handle parity as a known case rather than a surprise. The existence of that body of method is the best evidence that the Square-1 is a real puzzle and not just a disorienting one.

How Do You Approach One?

Get back to a cube first. Every workable method does this. Trying to solve colour while the shape is still wrong is how people lose an afternoon.

Count in thirty-degree units. A triangle is one unit and a kite is two. Thinking in those units rather than in faces makes legal turns predictable instead of a matter of trial.

Learn the parity case deliberately. It is not a sign you have gone wrong. It is a position the puzzle can genuinely reach, and it has its own fix.

Expect it to look worse before better. Shape restoration frequently passes through states more distorted than the scramble.

What Do We Make That Is Like This?

Nothing mechanical turns in our catalogue, so the honest comparison is to the idea rather than the object.

What a Square-1 shares with our range is that the shape is the problem. That is the premise of turning interlocking cubes, where a piece has to rotate past another and nothing is marked or coloured: EcstaTIC is two pieces and one rotation.

If you want the twisty puzzle we rate as most approachable, that is the Gear Cube, and the nearest colour-free cousin is the Mirror Cube.

The shelf is cube puzzles and the range is mechanical puzzles.

For a different kind of parity, one caused by missing centres rather than uneven pieces, see the Void Cube.

For shape-shifting without any difficulty attached, the Shashibo folds into more than seventy forms and resists you at none of them.

Frequently Asked Questions

What is a Square-1 puzzle?

A three-layer twisty puzzle whose top and bottom layers are cut into four kite-shaped corners and four triangular edges, with a middle layer of just two trapezoids. Because the pieces are different angular widths, the puzzle changes shape as it is turned.

Who invented the Square-1?

Karel Hršel and Vojtěch Kopský, in 1990. A Czechoslovak patent was filed on 8 November 1990 and a US design patent that December. It was originally sold as Back to Square One and later as Cube 21.

Why does the Square-1 change shape?

Because a kite piece occupies twice the angle of a triangle, so turning a layer can place a wide piece where a narrow one sat. On a standard cube every piece fills the same ninety degrees, which is why that puzzle keeps its shape.

Is the Square-1 harder than a Rubik's Cube?

Considerably, for most people. You have to restore the shape before you can address the colours, many turns are simply illegal until pieces align across the cut, and the two middle pieces can reach a parity state that needs its own algorithm.

How do you start solving a Square-1?

Get it back to a cube first, before touching colour. Count in thirty-degree units, where a triangle is one and a kite is two, so you can predict which turns are legal rather than discovering it by trial.