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CFOP Method
The CFOP METHOD (Cross – F2L – OLL – PLL), sometimes known as the FRIDRICH method, is one of the most commonly used methods in speedsolving a 3×3×3 Rubik\'s Cube . This method was first developed in the early 1980s combining innovations by a number of speed cubers. Czech speedcuber Jessica Fridrich is generally credited for popularizing it by publishing it online in 1997. The method works on a layer-by-layer system, first solving a cross typically on the bottom, continuing to solve the first two layers (F2L), orienting the last layer (OLL), and finally permuting the last layer (PLL). CONTENTS * 1 History * 2 The method * 3 Competition use * 4 References * 5 External links HISTORYBasic layer-by-layer methods were among the first to arise during the early 1980s cube craze. David Singmaster published a layer-based solution in 1980 which proposed the use of a cross
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Great Dodecahedron
In geometry , the GREAT DODECAHEDRON is a Kepler–Poinsot polyhedron , with Schläfli symbol
Schläfli symbol
{5,5/2} and Coxeter–Dynkin diagram
Coxeter–Dynkin diagram
of . It is one of four nonconvex regular polyhedra . It is composed of 12 pentagonal faces (six pairs of parallel pentagons), with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path. The discovery of the great dodecahedron is sometimes credited to Louis Poinsot
Louis Poinsot
in 1810, though there is a drawing of something very similar to a great dodecahedron in the 1568 book Perspectiva Corporum Regularium by Wenzel Jamnitzer
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Truncated Icosahedron
In geometry , the TRUNCATED ICOSAHEDRON is an Archimedean solid
Archimedean solid
, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons . It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller
Buckminster Fuller
pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb
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Muscle Memory
MUSCLE MEMORY has been used synonymously with motor learning , which is a form of procedural memory that involves consolidating a specific motor task into memory through repetition. When a movement is repeated over time, a long-term muscle memory is created for that task, eventually allowing it to be performed without conscious effort. This process decreases the need for attention and creates maximum efficiency within the motor and memory systems. Examples of muscle memory are found in many everyday activities that become automatic and improve with practice, such as riding a bicycle, typing on a keyboard, typing in a PIN , playing a musical instrument, poker martial arts or even dancing
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Tetrahedron
In geometry , a TETRAHEDRON (plural: TETRAHEDRA or TETRAHEDRONS), also known as a TRIANGULAR PYRAMID, is a polyhedron composed of four triangular faces , six straight edges , and four vertex corners . The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex , and may thus also be called a 3-SIMPLEX. The tetrahedron is one kind of pyramid , which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra , a tetrahedron can be folded from a single sheet of paper. It has two such nets
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Icosahedron
In geometry , an ICOSAHEDRON (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/ ) is a polyhedron with 20 faces. The name comes from Greek εἴκοσι (eíkosi), meaning 'twenty', and ἕδρα (hédra), meaning 'seat'. The plural can be either "icosahedra" (/-drə/ ) or "icosahedrons". There are many kinds of icosahedra, with some being more symmetrical than others. The best known is the Platonic , convex regular icosahedron
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Octahedron
In geometry , an OCTAHEDRON (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the REGULAR octahedron, a Platonic solid composed of eight equilateral triangles , four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube . It is a rectified tetrahedron . It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope . A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric
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Dodecahedron
In geometry , a DODECAHEDRON (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron , which is a Platonic solid
Platonic solid
. There are also three regular star dodecahedra , which are constructed as stellations of the convex form. All of these have icosahedral symmetry , order 120. The pyritohedron is an irregular pentagonal dodecahedron, having the same topology as the regular one but pyritohedral symmetry while the tetartoid has tetrahedral symmetry . The rhombic dodecahedron , seen as a limiting case of the pyritohedron, has octahedral symmetry . The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling . There are a large number of other dodecahedra
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Pattern Recognition
PATTERN RECOGNITION is a branch of machine learning that focuses on the recognition of patterns and regularities in data , although it is in some cases considered to be nearly synonymous with machine learning. Pattern recognition
Pattern recognition
systems are in many cases trained from labeled "training" data (supervised learning ), but when no labeled data are available other algorithms can be used to discover previously unknown patterns (unsupervised learning ). The terms pattern recognition, machine learning, data mining and knowledge discovery in databases (KDD) are hard to separate, as they largely overlap in their scope. Machine learning is the common term for supervised learning methods and originates from artificial intelligence , whereas KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use
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Panagiotis Verdes
PANAGIOTIS VERDES is the Greek inventor of the 6x6x6 , 7x7x7 , 8x8x8 and 9x9x9 Twisty Puzzles . He has also worked on new designs of every Twisty Puzzle from 2x2x2 to 11x11x11. INVENTIONS The V-Cube 6 in solved state The V-Cube 7 in solved state Prior to Verdes's invention, the 6x6x6 cube was thought to be impossible due to geometry constraints. Verdes's invention uses a completely different mechanism than the smaller Rubik's cubes; his mechanism is based on concentric, right-angle conical surfaces whose axes of rotation coincide with the semi-axes of the cube. The patents for the cubes were awarded in 2004, and mass-production began in 2008. Verdes's mechanism allows cubes of up to size 11x11x11, as larger cubes have geometrical constraints. REFERENCES * ^ A B C Slocum, Jerry (2009). The Cube: The Ultimate Guide to the World's Bestselling Puzzle. United States: Black Dog & Leventhal
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Cuboid
In geometry , a CUBOID is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube . While mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle ); this more restrictive type of cuboid is also known as a RECTANGULAR CUBOID, RIGHT CUBOID, RECTANGULAR BOX, RECTANGULAR HEXAHEDRON , RIGHT RECTANGULAR PRISM, or RECTANGULAR PARALLELEPIPED . CONTENTS * 1 General cuboids * 2 Rectangular cuboid * 2.1 Nets * 3 See also * 4 References * 5 External links GENERAL CUBOIDSBy Euler\'s formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula F + V = E + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces , 8 vertices , and 12 edges
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Algorithm
In mathematics and computer science , an ALGORITHM (/ˈælɡərɪðəm/ ( listen ) AL-gə-ridh-əm ) is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation , data processing and automated reasoning tasks. An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function . Starting from an initial state and initial input (perhaps empty ), the instructions describe a computation that, when executed , proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic ; some algorithms, known as randomized algorithms , incorporate random input
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Skewb Diamond
The SKEWB DIAMOND is an octahedron -shaped puzzle similar to the Rubik\'s Cube . It has 14 movable pieces which can be rearranged in a total of 138,240 possible combinations. This puzzle is the dual polyhedron of the Skewb
Skewb
. CONTENTS * 1 Description * 2 Number of combinations * 3 See also * 4 External links DESCRIPTIONThe Skewb
Skewb
Diamond has 6 octahedral corner pieces and 8 triangular face centers. All pieces can move relative to each other. It is a deep-cut puzzle; its planes of rotation bisect it. It is very closely related to the Skewb
Skewb
, and shares the same piece count and mechanism. However, the triangular "corners" present on the Skewb
Skewb
have no visible orientation on the Skewb
Skewb
Diamond, and the square "centers" gain a visible orientation on the Skewb
Skewb
Diamond
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Missing Link (puzzle)
MISSING LINK is a mechanical puzzle invented in 1981 by Steven P. Hanson and Jeffrey D. Breslow. The puzzle has four sides, each depicting a chain of a different color. Each side contains four tiles, except one which contains three tiles and a gap. The top and bottom rows can be rotated, and tiles can slide up or down into the gap. The objective is to scramble the tiles and then restore them to their original configuration. The two middle rows cannot be rotated. To move tiles in these rows, you need to loop the tiles from one row to another, up and down. There are 15 tiles and a gap, giving a maximum of 16! arrangements. However, the middle tiles of each four-tile chain are identical, and each position is equivalent to seven other positions obtained by rotating the entire puzzle (about its axis or upside-down), reducing the number of arrangements to 16! / 8 / 8 = 326,918,592,000
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Rubik's 360
RUBIK\'S 360 is a 3D mechanical puzzle released in 2009 by Ernő Rubik , the inventor of Rubik\'s Cube . Rubik's 360
Rubik's 360
was introduced on February 5, 2009 at the Nürnberg International Toy
Toy
Fair ahead of its worldwide release in August. The puzzle involves changing the position of six balls, each a different color, in a central sphere to six color-coded compartments in the outer sphere. This is done by maneuvering them through a middle sphere that only has two holes. There are three spheres that make up the puzzle. The puzzle begins with all 6 balls in the center; solving the puzzle involves getting the balls into the outer sphere. Unlike the original Rubik's Cube, there seem to be no algorithms and, in general, less mathematics associated with this puzzle. In addition there is a factor of manual dexterity involved in the solution that was unnecessary with the original cube
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Pyramorphix
The PYRAMORPHIX (/ˌpɪrəˈmɔːrfɪks/ , often misspelt Pyramorphinx) is a tetrahedral puzzle similar to the Rubik\'s Cube . It has a total of 8 movable pieces to rearrange, compared to the 20 of the Rubik's Cube. Though it looks like a simpler version of the Pyraminx
Pyraminx
, it is an edge-turning puzzle with the mechanism identical to that of the Pocket Cube . CONTENTS * 1 Description * 2 Number of combinations * 3 Master Pyramorphix
Pyramorphix
* 3.1 Solutions * 3.2 Number of combinations * 4 See also * 5 References * 6 External links DESCRIPTIONAt first glance, the Pyramorphix
Pyramorphix
appears to be a trivial puzzle. It resembles the Pyraminx, and its appearance would suggest that only the four corners could be rotated
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