Skip to content
Lizely

Cube Net Puzzle

Classify eight six-square patterns with a reproducible three-dimensional fold test and learn what makes a cube net valid.

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Inspect how the six edge-connected squares branch from one another and imagine each shared edge as a hinge.
  2. 2.Choose Yes, it folds or No, faces overlap; keyboard players can press Y or N for the same actions.
  3. 3.Classify all eight fixed nets for exactly 1,000 points before two incorrect answers deadlock the run.

About Cube Net Puzzle

Cube Net Puzzle presents eight arrangements made from six edge-connected squares and asks one focused question: will this pattern fold into a cube without two faces occupying the same side? Choose Yes or No for each arrangement. Every correct classification advances to the next fixed question and awards 125 points. Finish all eight questions for exactly 1,000 points. A wrong answer leaves the same pattern on screen so you can reconsider its hinges; two wrong answers end the run until you use Restart.

The puzzle is grounded in a complete combinatorial result rather than a hand-picked visual guess. A hexomino is a shape made by joining six equal squares edge to edge. When translations, rotations, and mirror images are treated as equivalent, there are 35 free hexominoes. Published mathematics references agree that exactly 11 of those shapes are nets of a cube. The evidence pack records all eleven valid shapes as canonical coordinate fixtures and links both the Wolfram MathWorld discussion of nets and an independent American Mathematical Society feature whose Figure 9 shows the complete set of eleven cube nets.

The game does not trust the fixture labels by themselves. Its local logic starts one square as a face pointing in the positive z direction. It then walks across every shared edge with breadth-first search. Moving east, west, north, or south rotates the neighboring square's right, down, and normal vectors by a quarter turn around the shared hinge. A pattern is valid only when all six cells are connected, every repeated traversal agrees on the same three-dimensional orientation, and the six final face normals are unique. Those normals must be the positive and negative x, y, and z directions of a cube.

An independent enumeration check grows polyominoes one edge at a time. Each candidate is normalized under translation and all eight planar symmetries, which collapses rotated and reflected copies to one canonical key. The test suite confirms that this process yields 35 distinct free hexominoes, that the folding algorithm accepts exactly 11, and that those 11 keys equal the sourced fixture table. It also rejects duplicate cells, disconnected six-cell inputs, and a two-by-three rectangle whose faces would overlap when folded.

The eight rounds are deterministic: four valid cube nets and four non-nets are selected from that complete 35-shape set in a stable order. A deterministic quiz is useful for release verification because local and production browser tests can submit the same answer sequence, observe the same intermediate states, and finish at the same 1,000-point score. There is no random seed, remote question feed, hidden daily rotation, or server answer call. Restart always restores question one, zero score, zero mistakes, and an unfrozen board.

You can play by touch, mouse, or keyboard. The two large answer controls are native buttons with visible focus behavior. Press Y when you believe the six squares fold into a cube, or N when you believe faces collide or fail to cover the cube. The diagram is an accessible SVG with a descriptive label, and the status line reports the current question and mistake count. All interactive targets remain comfortably sized on a narrow screen. The shared game shell supplies score persistence, Restart, and the double-Escape boss key.

The puzzle runs entirely in the browser as a React client island. It uploads no answer, requests no sensor permission, invokes no geometry service, and adds no package dependency. The coordinate tables are tiny integer pairs. Enumeration and fold checks operate on small sets and maps, so their cost is bounded and negligible on ordinary phones and laptops. Styling uses only Lizely's existing color, border, type, and surface tokens, keeping both light and dark themes readable without introducing a separate visual system.

Use the game as a short recreational exercise in imagining hinged faces. It can help explain why merely connecting six squares is not sufficient: folds may assign two cells to the same cube direction, or a loop may demand contradictory orientations. However, a score from eight fixed questions is not a spatial-ability test, educational placement exam, cognitive assessment, medical screening, or employment measure. Familiarity with cube nets, repeated play, device input, and guessing all affect results. The interface states this limitation plainly and should not be used to diagnose, rank, or label a person.

The content also avoids implying that every geometric net problem is solved by this specific checker. The embedded algorithm is intentionally scoped to six unit squares and a cube. It does not validate arbitrary polyhedron nets, tabs for physical papercraft, material thickness, cut tolerances, printable scale, or whether a real sheet can pass through itself during folding. For the stated six-square classification, though, the finite search, sourced eleven-net table, and orientation-based golden tests provide a reproducible answer rather than an intuition-only animation.

Methodology & sources

Enumerate free hexominoes by edge growth and canonicalize each candidate across translation and the eight rotations/reflections of the square grid. For a six-cell candidate, run BFS from one face with orthogonal right, down, and normal vectors; quarter-turn the basis across every shared edge, reject contradictory paths, and accept only six connected cells with six unique axis normals. The fixed quiz interleaves four accepted and four rejected canonical shapes, awards 125 for each correct answer, completes at 1,000, deadlocks on the second error, and ignores input after either terminal state.

Frequently asked questions

How many different cube nets are there?
There are 11 distinct cube nets when rotations and mirror images are treated as the same free shape.
How does the game decide whether a net works?
It propagates a three-dimensional orientation across every shared edge and requires six connected faces with six unique cube normals.
Can I play on a phone or without a mouse?
Yes. Use the large touch buttons, or press Y and N on a keyboard. Restart and the shared boss key are also available.
Is the score a spatial-ability diagnosis?
No. This is a fixed recreational puzzle, not a cognitive, medical, educational, or employment assessment.

Related tools

Mini Games guides

View all