Rubik's Cube
Enable an AI agent to recognise a Rubik's Cube, interpret its configuration and condition, and choose justified moves or interventions toward a stated goal.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
Researched by: Codex + Grok
Purpose and description
Enable an AI agent to recognise a Rubik's Cube, interpret its configuration and condition, and choose justified moves or interventions toward a stated goal.
A 3×3×3 face-turning cubic twisty puzzle, invented by Ernő Rubik in 1974, whose six faces rotate in multiples of 90° about three mutually orthogonal axes and thereby permute and orient eight corner cubies and twelve edge cubies around six centres, realising a group of 43,252,003,274,489,856,000 reachable configurations.
It can be Inspect additional faces and reconcile observations into a consistent configuration.; Validate a configuration against the declared piece inventory and turn rules.; Generate, explain or compare move sequences toward a declared target.; Execute permitted turns through a physical manipulator or simulation interface.; Verify a turn's result and replan when execution differs from the prediction.; Identify when further inspection or a separately authorised repair is needed..
Distinguishing features
For the baseline puzzle, each of six faces presents a 3×3 arrangement of facelets; a different order requires variant identification.
Turning a layer relocates connected groups of markings across faces while preserving piece membership; a cube-shaped colour display with independently changeable cells fails this test.
The baseline interpretation distinguishes centre, edge and corner pieces by their positions and exposed facelets; a sliding-tile puzzle has a different position and move structure.
Configuration changes must follow the declared turn rules; arbitrary facelet recolouring is an edit or intervention, not a puzzle move.
Appearance and move structure can establish compatibility with a conventional cube puzzle, but do not by themselves establish Rubik's branding or authenticity.
Scope
+ Identification of the puzzle's size, markings and move structure
+ Facelet observations and their interpretation as movable pieces
+ Current configuration, observation uncertainty and solved-state criteria
+ Permitted turns, move sequences and configuration transitions
+ Mechanical or interface conditions that affect puzzle manipulation
- General theory and classification of twisty puzzles
- Manufacturing, materials engineering and detailed component design
- Brand ownership, licensing and authenticity certification
- Competition administration, records and participant rankings
- A solver's general learning history or cognitive abilities
Characteristics
- Puzzle order
- Facelet positions per face edge; baseline 3 Determines whether the baseline piece interpretation and move rules apply.
- Representation medium
- Physical puzzle, interactive simulation, static depiction, unknown Separates objects that can be turned from representations that can only be inspected.
- Marking scheme
- Colours, symbols, pictures, mixed markings, unknown Determines how facelets are distinguished and whether orientation of markings affects completion.
- Observation frame
- Mapping between observed faces, puzzle-relative face labels and agent viewpoint Prevents a change of viewpoint from being mistaken for a puzzle move.
- Configuration knowledge
- Unobserved, partial, ambiguous, complete but unchecked, validated, inconsistent Controls whether an agent can plan a solution or must gather more observations.
- Turn reachability
- Reachable under declared rules, unreachable under declared rules, undetermined Distinguishes an ordinary scramble from an observation error or a configuration requiring intervention.
- Goal configuration
- Declared solved-state predicate or target pattern, including permitted whole-cube rotations Makes success testable without assuming every task asks for uniformly coloured faces.
- Manipulation readiness
- Ready, misaligned, obstructed, damaged, interface unavailable, unknown Determines whether a planned turn can be attempted and verified.
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 6 bundles · 11 layers · 18 findings · 31 questions.
Cube identity and boundaries Establish which cube puzzle or representation is being modelled and whether the baseline applies.
A cube-shaped object, a compatible twisty puzzle and a branded Rubik's product require different identity claims.
Puzzle structure
Identify face order and the arrangement that moves as a puzzle.
Baseline compatibility
Record the observed face layout and move structure before applying conventional 3×3×3 assumptions.
- Does each face have a 3×3 facelet layout, and which layers can turn? definition
- Which observed features require variant-specific rules instead of the baseline? boundary
Identity evidence
Separate the represented puzzle from its medium and product attribution.
Medium and attribution
Record whether the subject is a physical puzzle, executable simulation or depiction, and the evidence for any product identity.
- Can this subject actually perform puzzle turns, or does it only depict a configuration? boundary
- What markings, packaging or provider records support identifying it as a Rubik's Cube product? provenance
Facelets, pieces and observation Translate visible markings into a configuration with an explicit frame and known gaps.
A cube cannot be solved reliably from face colours unless observations agree about viewpoint and piece membership.
Face reference frame
Anchor face labels and distinguish viewpoint changes from changes within the puzzle.
Stable face labelling
Record how observations map to puzzle-relative faces throughout inspection and manipulation.
- Which observed faces establish the current up, front and right reference directions? definition
- After the cube or camera rotates, how will the agent preserve the identity of previously observed faces? action
Piece reconstruction
Associate facelets with pieces while retaining uncertainty.
Observed piece configuration
Record inferred centre, edge and corner identities, positions and orientations without silently filling unseen facelets.
- Which piece positions and orientations are established by the observations, and which remain ambiguous? measurement
- Which additional face views would distinguish the remaining candidate configurations? action
Configuration validity and goals Determine whether the interpreted state fits the puzzle rules and whether it satisfies the requested target.
An agent must distinguish a difficult scramble, an inconsistent observation and a completed puzzle.
Turn reachability
Assess configuration consistency and reachability under the selected rule set.
State consistency assessment
Keep inventory checks separate from the stronger claim that a configuration can be reached by permitted turns.
- Do the observed markings and reconstructed pieces match the declared puzzle inventory? measurement
- What validated checks establish reachability for this variant, and which checks have actually been applied? provenance
- If a check fails, what inspection can distinguish misreading from altered assembly or markings? action
Completion criteria
Define the requested target independently of a solver's informal judgement.
Explicit target predicate
Record which arrangements count as complete, including any picture orientation or display orientation requirement.
- Does completion require uniform faces, aligned pictures or symbols, or a specified target pattern? definition
- Are whole-cube rotations equivalent for this goal, or must the result face a specified direction? boundary
Turn language and planning Connect unambiguous move instructions to predicted configuration changes and task objectives.
A correct sequence becomes unusable if face labels, turn directions or sequence conventions are misinterpreted.
Move semantics
Declare the vocabulary and interpretation of individual moves.
Unambiguous turn instructions
Specify the moved layer, angle and viewing convention, and distinguish a face turn from reorienting the whole cube.
- Which notation and viewing convention define each turn's layer and direction? definition
- Which face, slice, wide or whole-cube moves are supported by this puzzle and executor? boundary
Sequence selection
Choose a move sequence appropriate to the known configuration, goal and executor.
Plan preconditions and objective
Record the starting-state assumptions, target and optimisation criterion behind a proposed sequence.
- Which configuration and reference frame must hold before this sequence begins? definition
- Should the sequence prioritise a declared move-count metric, execution reliability, speed or teachability? action
- What simulation or derivation supports the claim that this sequence reaches the target? provenance
Execution and intervention Relate planned turns to actual manipulation and handle departures from normal puzzle operation.
Physical resistance, missed interface actions and altered assembly can invalidate otherwise sound solving plans.
Turn execution feedback
Check readiness and compare actual results with predicted transitions.
Verified turn completion
Record whether a requested turn completed, stopped partway or affected a different layer.
- Are the relevant layers aligned and unobstructed, or does the simulation interface accept the intended move? measurement
- What observation confirms that the intended layer moved through the intended angle? measurement
- How should the agent stop, reobserve and update its configuration after a missed or unexpected turn? action
Non-turn interventions
Distinguish solving from changes to assembly, markings or simulated state.
Intervention boundary
Record resets, disassembly, piece reorientation or relabelling as interventions that require a new state assessment.
- Which proposed actions alter assembly, markings or stored state instead of applying a permitted puzzle turn? boundary
- Which interventions does the task authorise, and what observations must be repeated afterward? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Kinds and varieties
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Canonical 3×3×3 colour cube (the branded Rubik's Cube and its solid-colour equivalents)
- Speedcube (modern magnetized, tension- and compression-adjustable 3×3 competition hardware)
- Smart or connected 3×3 (on-board move sensing and app tracking)
- Original 1970s-1980s mechanism (early tile or sticker hardware, including the Hungarian Bűvös kocka)
- Mini or keychain 3×3
- Picture or promotional 3×3 (photographs, logos, or printed faces instead of solid colours)
- Stickerless factory-coloured 3×3 versus stickered 3×3
- 3×3 shape modification that keeps the same cubie orbits (Mirror Blocks, Fisher Cube, and similar)
- Which of these kinds and varieties hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Identifiers and schemes
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Wikidata - Q173154 - Item for the 3×3×3 Rubik's Cube as a puzzle type and cultural object.
- WCA event ID - 333 - World Cube Association event code for the 3×3×3 Cube; related events use 333oh, 333bf, 333fm, 333mbf.
- Hungarian patent - HU170062 - Rubik's original 1975 patent for the spatial logic toy later sold as Bűvös kocka.
- USPTO patent - US4378116 - United States patent 'Mechanical puzzle' corresponding to the Rubik mechanism.
- LCSH - Rubik's Cube - Library of Congress Subject Heading used in library and bibliographic records.
- Trademark - RUBIK'S (word mark, notably Nice Class 28) - Brand owned by Rubik's Brand Ltd (now under Spin Master); product SKUs additionally carry ordinary GTIN/EAN/UPC codes that are edition-specific, not type-level.
- Which of these identifiers and schemes hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Standards and regulation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- WCA Regulations and Guidelines (World Cube Association) - competition definition of a 3×3×3 Cube, scrambling, inspection, timing, and puzzle legality.
- EN 71 series (CEN) - European toy safety when the cube is placed on the market as a toy.
- ASTM F963 (ASTM International) - United States toy-safety specification applying to cubes sold as toys.
- ISO 8124 (International Organization for Standardization) - international toy-safety series used in many jurisdictions for the same goods.
- Consumer Product Safety Improvement Act / 16 CFR toy rules (United States Congress / CPSC) - children's-product duties when marketed to children, including tracking labels and, where relevant, small-part and magnet provisions.
- National trademark and design-right regimes (including a well-known EUIPO/General Court dispute over a 3D colour-combination mark) - they govern use of the name RUBIK'S and some product dress, not the mathematical puzzle itself.
- Which of these standards and regulation hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Real-world use
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Sold worldwide as a mass-market mechanical puzzle and desk toy.
- Used as the canonical event in World Cube Association speedsolving competitions (singles, averages, one-handed, fewest moves, and blindfolded).
- Used in mathematics teaching to exhibit a concrete finite group, algorithms, and parity constraints.
- Printed as promotional merchandise (logos and photographs on the six faces).
- Collected as design and toy-history objects, including museum holdings.
- Paired with apps via smart cubes for timed practice and move reconstruction.
- Disassembled and reassembled by hobbyists for lubrication, magnetising, and tension setup.
- Which of these real-world use hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Typical measurements
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Number of reachable configurations - 43252003274489856000 (exact) - positions
- God's number in the face-turn metric - 20 (maximum over all reachable positions) - face turns
- God's number in the quarter-turn metric - 26 (maximum over all reachable positions) - quarter turns
- Cubie edge length of a typical 3×3×3 - 55-57 (classic and most speedcubes); competition hardware commonly sits in a slightly wider band around that - mm
- Mass of a typical 3×3×3 - 70-120 - g
- Facelets (coloured stickers or tiles) - 54 (exact for a complete 3×3×3) - facelets
- Solve time after a standard scramble - world-class singles about 3-6; trained hobbyists often 10-40; untrained first solves from minutes to hours - s
- Which of these typical measurements hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Failure modes and hazards
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Piece pop or lock-up during a turn, sometimes leaving the cube in an illegal (unreachable) state that cannot be solved without disassembly.
- Sticker peeling or lost tiles, which destroy a unique colour reading of the state.
- Dried lubricant, over-tight tension, or debris causing poor corner cutting and mechanical freeze.
- Choking hazard from detached cubies or tiles in cubes marketed around young children.
- Ingestion hazard from small neodymium magnets used in many modern speedcubes.
- Counterfeit branded cubes with weak mechanisms and unauthorized RUBIK'S marking.
- Misassembly after a pop (odd corner twist, single-edge flip, or odd permutation), which is a user-induced unsolvable state rather than a defect of the group.
- Which of these failure modes and hazards hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Regional variation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Hungary: original name Bűvös kocka (Magic Cube); the inventor and early manufacture are Hungarian.
- German-speaking countries: commonly Zauberwürfel.
- Sinophone markets: generic name 魔方 (mófāng); branded Rubik's product is a minority of a large China-centred manufacturing industry (GAN, MoYu, QiYi, and others).
- Japan: ルービックキューブ; an older 'Japanese' colour scheme placed white opposite blue rather than yellow.
- Western factory scheme is usually white opposite yellow, red opposite orange, blue opposite green, with a fixed clockwise colour cycle; stickerless Chinese speedcubes popularised that scheme globally.
- English usage often genericizes 'Rubik's cube' to any NxN cube, while the trademark and WCA event 333 remain specifically 3×3×3.
- Which of these regional variation hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Pocket Cube (2×2×2) - Count layers on a face: two versus three; a 2×2 has only corner cubies and no edge cubies.
- Rubik's Revenge (4×4×4) and other even-order NxN cubes - Four or more layers per face; reduction introduces parity cases that cannot occur on a mechanically intact 3×3.
- Skewb - Deep-cut corner-turning cube: turns are about cube vertices, not face centres.
- Pyraminx - Tetrahedral puzzle with four axes; it is not cubic and has a different group.
- Square-1 - Middle-slice turns change the outline (shape-shifting); cubies are not uniformly cubic through a scramble.
- Megaminx - Dodecahedral analogue with twelve faces rather than six.
- Nichols Cube / other 2×2 magnetic or early cubic puzzles - Different mechanism and usually 2×2; they are historically adjacent patents, not the Rubik 3×3 face-turning core.
- Ordinary coloured cube or die - No face-turning mechanism and no cubie permutation group; faces do not rotate relative to a core.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of Rubik's Cube this model covers, and on what evidence? provenance
Sources
- Rubik's Cube - Invention date and original Hungarian name, mechanical anatomy, group order, trademarked product history, and common named variants.
- WCA Regulations - How the 3×3×3 is defined and constrained in competition, including event identity 333 and puzzle legality.
- The Diameter of the Rubik's Cube Group Is Twenty - God's number: every reachable position can be solved in at most 20 face turns; 26 in the quarter-turn metric.
- Rubik's Cube (Q173154) - Stable identifier and cross-links to patents, trademarks, and catalogue records.
- Notes on Rubik's Magic Cube - Early specialist description of cubie orbits, orientation rules, and the distinction between reachable and illegal assemblies.
- Hungarian patent HU170062 (spatial logic toy) - Primary legal identification of Rubik's 1975 filing of the mechanism later marketed as the Magic Cube / Rubik's Cube.
What the second pass must settle
- Does the registry intend this entry to cover the conventional 3×3×3 puzzle concept, branded Rubik's products, or a broader family of sizes and variants?
- How should ownership be divided between this INF / INF.MED entry and any existing physical-object or interactive-simulation models?
- Which authoritative sources should establish the baseline move conventions and complete configuration-reachability checks?
- Which picture, symbol, tactile or shape-changing variants belong within this entry, and how do their completion criteria differ?
- Does an existing Vercy world model already own this concept or any proposed bundle that should be linked instead of duplicated?