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Jessica Fridrich
JESSICA FRIDRICH is a professor at Binghamton University , who specializes in data hiding applications in digital imagery. She is also known for documenting and popularizing the CFOP method, one of the most commonly used methods for speedsolving the Rubik\'s Cube , also known as speedcubing . She is considered as one of the pioneers of speedcubing, along with Lars Petrus . Nearly all of the fastest speedcubers have based their methods on Fridrich's, usually referred to as CFOP (Cross, First 2 Layers, Orient Last Layer, Permuting Last Layer). The method describes solving the cube in a layer-by-layer fashion. First a so-called "cross" is made on the first layer, consisting of the center piece and four edges. The first layer corners and edges of the second layer are put into their correct positions simultaneously (four pairs)
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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
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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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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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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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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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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Great Dodecahedron
In geometry , the GREAT DODECAHEDRON is a Kepler–Poinsot polyhedron , with Schläfli symbol {5,5/2} and 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 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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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
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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Hindawi Publishing Corporation
HINDAWI PUBLISHING CORPORATION is a commercial publisher of scientific, technical, and medical (STM) literature. Founded in 1997, Hindawi currently publishes more than 400 peer-reviewed scientific journals as well as a number of scholarly monographs , with an annual output reaching 22,000 articles in 2012. As of October 2014 , 11% of the journals were indexed in the Science Citation Index Expanded . The company has its headquarters in Cairo
Cairo
and a virtual office address in New York City
New York City
. Since 2007, all of Hindawi's journals have been open access and published under a Creative Commons Attribution License (CC-BY). Hindawi has been criticized for some of its editorial practices – including an alleged reliance on staff vetting of submissions rather than peer review by academics – and for its use of email spam in soliciting editorial board memberships and manuscripts
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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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Binghamton University
The STATE UNIVERSITY OF NEW YORK AT BINGHAMTON, commonly referred to as BINGHAMTON UNIVERSITY, is a public research university with campuses in Binghamton , Vestal , and Johnson City , New York , United States . Since its establishment as Triple Cities College
College
in 1946, the school has evolved from a small liberal arts college to a large doctoral-granting institution. Presently consisting of eight colleges and schools, it is now home to more than 17,000 undergraduate and graduate students. Binghamton is one of the four university centers in the State University of New York (SUNY) system. Binghamton University
University
is currently ranked 86th among the 201 national universities in U.S. News ">'s 2017 America's Best Colleges and Universities ranking; internationally, it is ranked in the cohort 801–1000 according to QS University
University
Rankings for 2018
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Czech Republic
The CZECH REPUBLIC (/ˈtʃɛk rᵻˈpʌblɪk/ ( listen ) CHEK-rə-PUB-lik ; Czech : Česká republika, Czech pronunciation: ( listen )), also known as CZECHIA (/ˈtʃɛkiə/ ( listen ), CHEK-ee-ə ; Czech : Česko, pronounced ( listen )), is a nation state in Central Europe
Europe
bordered by Germany
Germany
to the west, Austria
Austria
to the south, Slovakia
Slovakia
to the east and Poland
Poland
to the northeast. The Czech Republic
Czech Republic
covers an area of 78,866 square kilometres (30,450 sq mi) with a mostly temperate continental climate and oceanic climate . It is a unitary parliamentary republic , has 10.5 million inhabitants and the capital and largest city is Prague
Prague
, with over 1.2 million residents
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Czech Technical University In Prague
CZECH TECHNICAL UNIVERSITY IN PRAGUE (Czech : České vysoké učení technické v Praze, ČVUT) is one of the largest universities in the Czech Republic, and is one of the oldest institutes of technology in Central Europe
Central Europe
. It is also the oldest non-military technical university in Europe. In the academic year 2012/2013 8 faculties and 1 university institute of Czech Technical University
University
offered 105 degree programs and 419 fields of study, which enrolled more than 24,500 students
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Pyraminx Crystal
The PYRAMINX CRYSTAL is a dodecahedral puzzle similar to the Rubik\'s Cube and the Megaminx
Megaminx
. It is manufactured and sold by Uwe Mèffert in his puzzle shop since 2008. The puzzle was originally called the Brilic, and was first made in 2006 by Aleh Hladzilin, a member of the Twisty Puzzles Forum. It is not to be confused with the Pyraminx
Pyraminx
, which is also invented and sold by Meffert. CONTENTS * 1 History * 2 Description * 3 Solutions * 4 Number of combinations * 5 See also * 6 References HISTORY White-bodied Pyraminx
Pyraminx
Crystal with a star pattern applied to the faces. The Pyraminx
Pyraminx
Crystal was patented in Europe on July 16, 1987. The patent number is DE8707783U. In late 2007, due to requests by puzzle fans worldwide, Uwe Mèffert began manufacturing the puzzle. The puzzles were first shipped in February 2008
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Megaminx
The MEGAMINX (/ˈmɛɡəmɪŋks/ or /ˈmeɪ-/ ) is a dodecahedron -shaped puzzle similar to the Rubik\'s Cube . It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's Cube. CONTENTS * 1 History * 2 Description * 3 Solutions * 4 Variations * 5 Number of combinations * 6 Records * 6.1 Top 5 solvers by single solve * 6.2 Top 5 solvers by average of 5 solves * 7 See also * 8 References * 9 External links HISTORYThe Megaminx, or Magic Dodecahedron, was invented by several people independently and produced by several different manufacturers with slightly different designs. Uwe Mèffert eventually bought the rights to some of the patents and continues to sell it in his puzzle shop under the Megaminx
Megaminx
moniker. It is also known by the name Hungarian Supernova, invented by Dr. Cristoph Bandelow. His version came out first, shortly followed by Meffert's Megaminx
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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 , 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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