About Cubes
Open-Source Twisty Puzzle Wiki · Zero-Hallucination Standard
An encyclopedic, citation-backed reference for twisty puzzles — from Mirror Blocks to Megaminx — covering mechanical anatomy, group-theory permutation counts, and every major speedcubing methodology. All historical claims and records link to verifiable open-source sources.
Puzzle Catalog
Mirror Blocks (Mirror Cube)
IntermediateShape-Shifting 3×3 Variant — Solved by Shape, Not Color
The Mirror Cube is a 3×3×3 twisty puzzle where all pieces are uniform silver or gold — there are no colored stickers. Instead, each piece has unique physical dimensions: corners range from thin slivers to fat blocks, and the puzzle is scrambled by shape, not by color. When scrambled, the cube becomes an irregular, asymmetric blob; the solved state is a perfect rectangular cuboid.
The internal mechanism is identical to a standard 3×3×3. This means all CFOP, Roux, and LBL algorithms apply directly — you simply match heights and thicknesses instead of colors. The offset screw mechanism shifts the entire layer grid off-center, giving each of the 26 external pieces a unique size.
📐 Key Insight: The 8 corners have 8 distinct dimensions. The 12 edges are grouped into 3 thickness bands (thin at 1.6cm, medium at 2.0cm, thick at 2.4cm in a standard mirror cube). The 6 centers are flat discs.
Standard 3×3×3 Rubik's Cube
IntermediateThe Classic — Invented by Ernő Rubik in 1974
The iconic 3×3×3 has 43.25 quintillion possible permutations. Despite this staggering number, God's Number — the maximum moves required to solve any state using an optimal algorithm — is 20 moves (in Half-Turn Metric). This was proven in 2010 by Rokicki, Kociemba, Davidson, and Dethridge using 35 CPU-years of computation donated by Google.
The cube has 8 corner pieces (3 orientations each), 12 edge pieces (2 orientations each), and 6 fixed center pieces (defining face colors). Its state space forms a group under the Rubik's Group: a subgroup of the symmetric group S₄₈ with order 43,252,003,274,489,856,000.
2×2×2 Pocket Cube
BeginnerCorner-Only Permutation — Deceptively Deep
The 2×2 has no edge or center pieces — only the 8 corners of a 3×3. By fixing one corner (removing orientation redundancy), the state space reduces to 3,674,160 permutations. God's Number for the 2×2 is 11 moves (QTM) or 14 moves (HTM).
Despite its smaller size, the 2×2 is a popular speedcubing event. The current WR single stands at 0.43s (Teodor Fridlund, 2024). Common methods include Ortega (2-look LL), CLL (1-look LL with 42 algorithms), and EG (full 1-look with ~128 algorithms).
4×4×4 & 5×5×5 Big Cubes
AdvancedRubik's Revenge & Professor's Cube — Parity Phenomena
Big cubes introduce parity errors not possible on a 3×3. The 4×4 can reach states with an odd permutation of edges — requiring OLL parity (single edge flip) or PLL parity (adjacent edge swap) corrections. These arise because 4×4 edge pieces appear identical and can be paired in two orientations.
The standard big cube method is Reduction: pair all edge trios into "dedges", solve centers, then treat the cube like a 3×3 — handling any parity corrections that arise. Advanced solvers use Yau (cross-first) or Hoya method to reduce parity frequency.
Pyraminx
BeginnerTetrahedral Rotational Puzzle
The Pyraminx is a tetrahedron-shaped puzzle with 4 tips, 4 center faces, 6 edges. The 4 tips are trivially solved by rotation. The 4 centers are fixed and define orientation. The 6 edges must be permuted and oriented — giving 75,582,720 states (tips excluded).
God's Number for the Pyraminx is 11 moves (QTM). Common methods include V-First (layer by layer) and Top-First with 1-look last-layer (L4E — Last 4 Edges). The WR single is sub-1 second.
Megaminx
AdvancedDodecahedral Twisty Puzzle — 12 Faces
The Megaminx has 12 pentagonal faces, 20 corner pieces, 30 edge pieces, and 12 center pieces. Its gargantuan state space of ~10⁶⁸ dwarfs even the 5×5. Despite this, it is solved layer-by-layer similarly to a 3×3 — the last layer features star parity (5 edges around a face) rather than cross parity.
CFOP concepts transfer directly: first two layers use F2L-style pair insertion, and the last layer requires OLL and PLL equivalents adapted for pentagonal symmetry.
Skewb
BeginnerDeep-Cut Corner-Turning Cube
The Skewb rotates around its 4 body diagonals rather than face axes — making it a deep-cut puzzle. It has only 6 center pieces (fixed in position, free to rotate) and 8 corner pieces. The state space of 3,149,280 makes it one of the smallest non-trivial puzzles.
Common methods: Sarah's Advanced Method (corners-first then centers) and Meeus Method. The WR single is 0.93s (Will Callan, 2023).
Square-1
ExpertShape-Shifting Geometry-Changing Puzzle
The Square-1 is unique: turns can change the shape of the entire puzzle, transforming it into non-cubic forms with kite and triangular pieces. The middle layer can flip 180°, further complicating state space.
Solving requires: cubification (restore cubic shape), then top/bottom alignment, then handle parity (zig-zag parity). Advanced methods like Vandenbergh-Harris use commutators and conjugates to achieve sub-10s times. The WR single is 3.68s.
🧩Solving Methodologies
CFOP — Fridrich Method
Cross · F2L · OLL · PLL
The most popular competitive method, developed by Jessica Fridrich in the 1980s and documented publicly in 1997. CFOP stands for Cross, F2L, OLL, PLL. It dominates at the highest levels of speedcubing — the majority of sub-10s solvers use CFOP. Full CFOP requires memorizing 78 algorithms (57 OLL + 21 PLL) but can be learned incrementally with 2-look variants.
Cross
Solve 4 edge pieces on the bottom layer, aligned with center colors. Typically planned during the 15s inspection phase.
F2L (First Two Layers)
Pair and insert 4 corner-edge pairs into their slots simultaneously. 41 cases — most solved intuitively.
OLL (Orientation Last Layer)
Orient all 9 top-face stickers yellow-up using 57 algorithms (2-look: 9 algs).
PLL (Permutation Last Layer)
Permute the correctly-oriented last layer pieces into their final positions. 21 algorithms (2-look: 6 algs).
Roux Method
First Block · Second Block · CMLL · LSE
Invented by Gilles Roux in 2003. Roux is a block-building method that relies heavily on M-slice turns, making it particularly mouse-hand efficient. It generates fewer moves on average than CFOP and has grown in popularity among top speedcubers (e.g., Kian Mansour, Sean Patrick Villanueva). The last step (LSE) is entirely M/U moves — no R or L turns — making it ideal for one-handed solving.
First Block (FB)
Build a 1×2×3 block on the left side (DL column + back edge), intuitively.
Second Block (SB)
Build a 1×2×3 block on the right side while preserving the left block, using R and M moves.
CMLL
Orient and permute the 4 top corners, ignoring M-slice. 42 algorithms.
LSE (Last Six Edges)
Solve all remaining 6 edges in the M-slice and top layer using only M and U moves.
ZZ Method
EOLine · ZZF2L · OCLL/PLL or ZBLL
Invented by Zbigniew Zborowski in 2006. ZZ begins by fully orienting all 12 edges and placing the DF/DB edges simultaneously (EOLine). This eliminates all cube rotations during F2L (only R, L, U turns needed) and guarantees an OLL-free last layer (edges are always correctly oriented). Advanced practitioners use ZBLL (1-look LL with ~493 algorithms) for the fastest possible completion.
EOLine
Orient all 12 edges and place DF/DB edges simultaneously. Typically 6-9 moves.
ZZF2L
Solve the first two layers using only R, U, L moves — no cube rotations required.
OCLL + PLL
Standard OLL (corners only, since edges are oriented) then PLL. Or ZBLL for 1-look LL.
Beginner's Layer-by-Layer (LBL)
White Cross → Corners → Middle → Yellow Cross → Last Layer
The most intuitive method for beginners, requiring only 5 core algorithms. It solves the cube one layer at a time from bottom to top. While inefficient in move count (~100–120 STM), it is the recommended first approach for anyone starting their speedcubing journey, as it builds a strong spatial intuition of how the cube behaves.
White Cross
Place 4 white edges on the bottom face, aligned with side centers.
White Corners
Insert 4 white corner pieces to complete the first layer using the classic right-hand or left-hand algorithm.
Middle Layer Edges
Insert 4 middle-layer edges (non-yellow) using F2L-adjacent insert algorithms.
Yellow Cross
Orient top edges to form a yellow cross using the "fish" algorithm.
Last Layer
Orient yellow corners (Sune/Anti-Sune), then permute corners and edges with A-perm and U-perm.
Blindfolded Solving (BLD)
Memorization · Cycle Notation · Old Pochmann / 3-Style
Blindfolded solving requires full memorization of the cube's state before donning a blindfold, then executing a planned solution with zero visual feedback. It applies cycle notation from group theory: the solver identifies a sequence of 3-cycles (commutators) that move pieces between buffer slots and target positions. The classic method is Old Pochmann (T-perm for edges, Y-perm for corners). Advanced solvers use3-Style — 3-cycle commutators for both corners and edges — achieving sub-20s BLD times.
Memorization
Assign letter codes to each piece position (e.g., A-X for edges). Memorize the letter sequence as a story or image using memory palaces.
Edge Cycle Execution
Using Old Pochmann: execute T-perm conjugates to cycle each edge through the UF buffer slot.
Corner Cycle Execution
Using Old Pochmann: execute Y-perm conjugates for each corner through the UFR buffer.
Parity Handling
If an odd number of cycles exist, a parity algorithm (T+Y) is applied between edges and corners.