## Yottaminx Solved Assignment

1. Dodecahedron – In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the dodecahedron, which is a 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 a pentagonal dodecahedron, having the same topology as the regular one. The rhombic dodecahedron, seen as a 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. The convex regular dodecahedron is one of the five regular Platonic solids, the dual polyhedron is the regular icosahedron, having five equilateral triangles around each vertex. Like the regular dodecahedron, it has twelve pentagonal faces. However, the pentagons are not constrained to be regular, and its 30 edges are divided into two sets – containing 24 and 6 edges of the same length. The only axes of symmetry are three mutually perpendicular twofold axes and four threefold axes. Note that the regular dodecahedron can occur as a shape for quasicrystals with icosahedral symmetry. Its name comes from one of the two common crystal habits shown by pyrite, the one being the cube. The coordinates of the eight vertices of the cube are, The coordinates of the 12 vertices of the cross-edges are. When h =1, the six cross-edges degenerate to points, when h =0, the cross-edges are absorbed in the facets of the cube, and the pyritohedron reduces to a cube. When h = √5 − 1/2, the inverse of the golden ratio, a reflected pyritohedron is made by swapping the nonzero coordinates above. The two pyritohedra can be superimposed to give the compound of two dodecahedra as seen in the image here, the regular dodecahedron represents a special intermediate case where all edges and angles are equal. A tetartoid is a dodecahedron with chiral tetrahedral symmetry, like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices. However, the pentagons are not regular and the figure has no fivefold symmetry axes, although regular dodecahedra do not exist in crystals, the tetartoid form does

2. Rubik's Cube – Rubiks Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. As of January 2009,350 million cubes had been sold making it the worlds top-selling puzzle game. It is widely considered to be the worlds best-selling toy, in a classic Rubiks Cube, each of the six faces is covered by nine stickers, each of one of six solid colours, white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is green, and orange is opposite red. On early cubes, the position of the colours varied from cube to cube, an internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have one colour. Similar puzzles have now produced with various numbers of sides, dimensions. Although the Rubiks Cube reached its height of popularity in the 1980s, it is still widely known. Many speedcubers continue to practice it and other twisty puzzles and compete for the fastest times in various categories, since 2003, The World Cube Association, the Rubiks Cubes international governing body, has organised competitions worldwide and kept the official world records. In March 1970, Larry D. Nichols invented a 2×2×2 Puzzle with Pieces Rotatable in Groups, Nicholss cube was held together with magnets. Patent 3,655,201 on April 11,1972, on April 9,1970, Frank Fox applied to patent his Spherical 3×3×3. He received his UK patent on January 16,1974, in the mid-1970s, Ernő Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest. He did not realise that he had created a puzzle until the first time he scrambled his new Cube, Rubik obtained Hungarian patent HU170062 for his Magic Cube in 1975. Rubiks Cube was first called the Magic Cube in Hungary, Ideal wanted at least a recognisable name to trademark, of course, that arrangement put Rubik in the spotlight because the Magic Cube was renamed after its inventor in 1980. The first test batches of the Magic Cube were produced in late 1977, Magic Cube was held together with interlocking plastic pieces that prevented the puzzle being easily pulled apart, unlike the magnets in Nicholss design. With Ernő Rubiks permission, businessman Tibor Laczi took a Cube to Germanys Nuremberg Toy Fair in February 1979 in an attempt to popularise it. It was noticed by Seven Towns founder Tom Kremer and they signed a deal with Ideal Toys in September 1979 to release the Magic Cube worldwide, the puzzle made its international debut at the toy fairs of London, Paris, Nuremberg and New York in January and February 1980. After its international debut, the progress of the Cube towards the toy shop shelves of the West was briefly halted so that it could be manufactured to Western safety, a lighter Cube was produced, and Ideal decided to rename it

3. Parity (mathematics) – Parity is a mathematical term that describes the property of an integers inclusion in one of two categories, even or odd. An integer is even if it is divisible by two and odd if it is not even. For example,6 is even there is no remainder when dividing it by 2. By contrast,3,5,7,21 leave a remainder of 1 when divided by 2, examples of even numbers include −4,0,8, and 1738. In particular, zero is an even number, some examples of odd numbers are −5,3,9, and 73. Parity does not apply to non-integer numbers and this classification applies only to integers, i. e. non-integers like 1/2,4.201, or infinity are neither even nor odd. The sets of even and odd numbers can be defined as following and that is, if the last digit is 1,3,5,7, or 9, then it is odd, otherwise it is even. The same idea will work using any even base, in particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0. In an odd base, the number is according to the sum of its digits – it is even if. The following laws can be verified using the properties of divisibility and they are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic, however, subtraction in modulo 2 is identical to addition, so subtraction also possesses these properties, which is not true for normal integer arithmetic. The structure is in fact a field with just two elements, the division of two whole numbers does not necessarily result in a whole number. For example,1 divided by 4 equals 1/4, which is neither even nor odd, since the concepts even, but when the quotient is an integer, it will be even if and only if the dividend has more factors of two than the divisor. The ancient Greeks considered 1, the monad, to be neither odd nor fully even. It is this, that two relatively different things or ideas there stands always a third, in a sort of balance. Thus, there is here between odd and even numbers one number which is neither of the two, similarly, in form, the right angle stands between the acute and obtuse angles, and in language, the semi-vowels or aspirants between the mutes and vowels. A thoughtful teacher and a pupil taught to think for himself can scarcely help noticing this, integer coordinates of points in Euclidean spaces of two or more dimensions also have a parity, usually defined as the parity of the sum of the coordinates. For instance, the cubic lattice and its higher-dimensional generalizations

4. Metric prefix – A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used

5. Alexander's Star – Alexanders Star is a puzzle similar to the Rubiks Cube, in the shape of a great dodecahedron. Alexanders Star was invented by Adam Alexander, an American mathematician and it was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties, painted surfaces or stickers, since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition. The puzzle has 30 moving pieces, which rotate in star-shaped groups of five around its outermost vertices. The purpose of the puzzle is to rearrange the pieces so that each star is surrounded by five faces of the same color. This is equivalent to solving just the edges of a six-color Megaminx and this is an odd puzzle to solve, and never really looks complete unless you know what youre looking for. The puzzle is solved when each pair of planes is made up of only one colour. To see a plane, however, you have to look past the five pieces on top of it, there are 30 edges, each of which can be flipped into two positions, giving a theoretical maximum of 30. ×230 permutations. This value is not reached for the reasons, Only even permutations of edges are possible. The orientation of the last edge is determined by the orientation of the other edges, since opposite sides of the solved puzzle are the same color, each edge piece has a duplicate. It would be impossible to swap all 15 pairs, so a reducing factor of 214 is applied, the orientation of the puzzle does not matter, dividing the final total by 60. There are 60 possible positions and orientations of the first edge and this gives a total of 30. ×215120 ≈7.24 ×1034 possible combinations, the precise figure is 72431714252715638411621302272000000. Rubiks Cube Combination puzzles Mechanical puzzles Description and solution

6. Impossiball – The Impossiball is a rounded icosahedral puzzle similar to the Rubiks Cube. It has a total of 20 movable pieces to rearrange, same as the Rubiks Cube, william O. Gustafson applied for a patent for the Impossiball design in 1981 and it was issued in 1984. Uwe Mèffert eventually bought the rights to some of the patents, the Impossiball is made in the shape of an icosahedron that has been rounded out to a sphere, and has 20 pieces, all of them corners. The puzzle has twelve circles located at the vertices of the icosahedron, because of the rounded shape of the puzzle, the pieces move up and down as they are rotated. It is also possible to one piece, turning the puzzle into a spherical version of the 15 puzzle. The purpose of the puzzle is to scramble the colors, and this puzzle is equivalent to solving just the corners of a Megaminx. The original Impossiball had the colors as the Rubiks Cube, red, orange, yellow, green, blue. Meffert currently produces two versions, one with six colors and one with twelve, the six-color version uses pink, two shades of orange, yellow, green and blue. All the pieces are still distinguishable, however, because the two pieces with the three colors are mirror images of each other. The twelve-color version has red, pink, orange, yellow, in spite of its daunting appearance and greater number of possible positions, the Impossiball is not much more difficult than the standard 2×2×2 Pocket Cube. This is because it is not a deep-cut puzzle, it only has pentagonal face layers which are similar in structure to the face layers of the cube. There are no pieces that do not have a counterpart on the cube, many of the techniques employed in the solution of the Pocket Cube can also be adapted for the Impossiball. There are 20. /2 ways to arrange the pieces, since there is no way to create odd permutations without tampering with the puzzle, there are 319 ways to orient the pieces, since the orientation of the last depends on that of the preceding ones. Since the Impossiball has no fixed face centers, this result is divided by 60, there are 60 possible positions and orientations of the first corner, but all are equivalent because of the lack of face centers. ×319120 ≈2.36 ×1025 The entire number is 23563902142421896679424000, Rubiks Cube Megaminx Dogic Alexanders Star Tuttminx Combination puzzles Mefferts puzzle shop Jaaps Impossiball page — contains solutions and other information

7. Pyraminx Crystal – The Pyraminx Crystal is a dodecahedral puzzle similar to the Rubiks Cube and the 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, which is also invented, the Pyraminx Crystal was patented in Europe on July 16,1987. In late 2007, due to requests by fans worldwide. The puzzles were first shipped in February 2008, there are two 12-color versions, one with the black body commonly used for the Rubiks Cube and its variations, and one with a white body. The puzzle company QJ started manufacturing this puzzle in 2010, leading Mefferts Puzzles to file a lawsuit against QJ, the Pyraminx Crystal ran out of stock fairly quickly, and became a collectors puzzle. In October 2011, a new set was created with some improvements to the quality. The puzzle consists of a dodecahedron sliced in such a way that the meet at the center of each pentagonal face. This cuts the puzzle into 20 corner pieces and 30 edge pieces, each face consists of five corners and five edges. When a face is turned, these pieces and five additional edges move with it, each corner is shared by 3 faces, and each edge is shared by 2 faces. By alternately rotating adjacent faces, the pieces may be permuted, the goal of the puzzle is to scramble the colors, and then return it to its original state. The puzzle is essentially a version of the Megaminx. The edge pieces can then be permuted by a simple 4-twist algorithm, R L R L and this can be applied repeatedly until the edges are solved. There are 30 edge pieces with 2 orientations each, and 20 corner pieces with 3 orientations each, however, this limit is not reached because, Only even permutations of edges are possible, reducing the possible edge arrangements to 30. /2. The orientation of the last edge is determined by the orientation of the other edges, Only even permutations of corners are possible, reducing the possible corner arrangements to 20. /2. The orientation of the last corner is determined by the orientation of the other corners, the orientation of the puzzle does not matter, dividing the final total by 60. There are 60 possible positions and orientations of the first corner and this gives a total of 30. ×31960 ≈1.68 ×1066 possible combinations, the full figure is 1677826942558722452041933871894091752811468606850329477120000000000

8. Tony Fisher (puzzle designer) – Tony Fisher is a British puzzle designer, who specialises in creating custom rotational puzzles. He is acknowledged by cubing enthusiasts as a pioneer in the creation of new puzzle designs, Fisher first began creating puzzles in 1981, when he modified two existing Rubik’s cubes by joining them along one edge to create a new device called the Siamese cube. This has been accredited as the first example of a “handmade modified rotational puzzle”, in 1995 Fisher further modified the conventional rotational puzzle design by shifting its cutting planes to create a 3x3x4 cube. This invention was further adapted in the creation of 2x3x4, 3x3x5 and 4x4x5 cube puzzles, another technique, initially developed by Geert Hellings, rounded the centre piece of a conventional 4x4x4 cube to create additional turning layers for a uniform 2x2x4, 6x6x6 and non-uniform 2x2x6. Fisher’s Golden Cubes, initially intended to be released as the Millennium Cube, the Golden Cube is considered to be Fisher’s most unusual contribution to the design of new combination puzzles, and has been mass-produced by Uwe Meffert. Since 1981 Fisher has designed and crafted around 100 puzzles based on different puzzle mechanisms, as well as puzzle manufacturing, he has also worked for Suffolk County Council as an archaeologist. Examples of Fisher’s puzzle designs can be found at the Puzzle Museum, including his Cylinder Cube, Golden Cube, Hexagonal Prism, Truncated Octaminx, official website Puzzle Museum Tonny Fisher Rotational Puzzles

9. Void Cube – The Void Cube is a 3-D mechanical puzzle similar to a Rubiks Cube, with the notable difference being that the center cubies are missing, which causes the puzzle to resemble a level 1 Menger sponge. The core used on the Rubiks Cube is also absent, creating holes straight through the cube on all three axes, due to the restricted volume of the puzzle it employs an entirely different structural mechanism from a regular Rubiks Cube, though the possible moves are the same. The Void Cube was invented by Katsuhiko Okamoto, gentosha Education, in Japan, holds the license to manufacture Void Cubes. The Void Cube is slightly more difficult than a regular Rubiks Cube due to parity, the lack of center cubes alters the parity considerations. A 90˚ rotation of a face either on the regular Rubiks Cube or on the Void Cube swaps the positions of eight cubes in two, odd parity, four cycles, overall, a face turn is an even permutation. On the regular cube a 90˚ rotation of the whole cube about a principal axis swaps the positions of 24 cubes in six, odd parity, on the regular cube a whole cube rotation is an even permutation. On the other hand, lacking center cubes, a 90˚ whole cube rotation on the Void Cube swaps 20 cubes in five, odd parity, thus, a whole cube rotation on the Void Cube is an odd permutation. In consequence, on the Void Cube turning the faces of the cube together with whole cube rotations can produce an arrangement where two cubes are swapped and the rest are in their original positions. This and other odd parity arrangements are not possible on the regular Rubiks Cube and these permutations are solvable with a number of simple algorithms. To see the relationship between parity on the cube and the void cube consider the regular cube. A regular cube solution takes a scrambled cube to the identity cube where the color of all the edge, a void cube solution takes a scrambled cube to an arrangement where the color of the edge and corner facelets match each other regardless of the color of the center facelet. These cats eye arrangements are formed by rotating the edge and corner cubes as a whole with respect to the center cubies and this may be done in 24 different ways but because of parity only 12 may be formed by turning the faces of the cube. Odd parity void cube positions are formed on odd parity cats eye regular cube positions, part of the interior of each hole is the inside surface of these pieces. Say that one of them is lying separately on a work surface, if you look straight down at one of these pieces its exterior is also square. Seen from an oblique position, however, each side of a square piece is somewhat akin to a low arch that joins neighboring corners. The low part of that arch engages mostly-hidden internal sliding pieces that support the edge cubies, the high surface of the arch includes convex curved circular flanges that engage grooves inside the cubies, to hold the structure together. When all faces of the puzzle are in their normal aligned state, each one is free to rotate without any obstruction from the other five pieces. When a face is rotated, its own square piece also rotates with that faces cubies, what retains the cubies when a face is rotated is the set of four curved flanges on the four neighboring square-hole pieces

10. Speedcubing – Speedcubing is the activity of solving a variety of twisty puzzles, the most famous being the Rubiks Cube, as quickly as possible. For most puzzles, solving entails performing a series of moves that alters a scrambled puzzle into a state in every face of the puzzle is a single. Some puzzles have different requirements to be considered solved, such as the Clock, the current record for a single solve is held by Feliks Zemdegs, who presented a 4.73 second solve at the POPS Open 2016 in December 2016. Feliks Zemdegs also holds the record for the average of five solves at 6.45 seconds. Speedcubing is an activity among the international Rubiks Cube community. Members come together to hold competitions, work to develop new solving methods, the Rubiks Cube was invented in 1974 by Hungarian professor of architecture, Ernő Rubik. A widespread international interest in the began in 1980, which soon developed into a global craze. On June 5,1982, the first world championship was held in Budapest,19 people competed in the event and the American Minh Thai won with a single solve time of 22.95 seconds. Other notable attendees include Jessica Fridrich and Lars Petrus, two people who would later be influential in the development of solving methods and the speedcubing community. The height of the Rubiks Cube craze began to fade away after 1983 and this revival of competition sparked a new wave of organized speedcubing events, which include regular national and international competitions. There were twelve competitions in 2004,58 more from 2005 to 2006, over 100 in 2008, there have been seven more World Championships since Budapests 1982 competition, which are traditionally held every other year, with the most recent in São Paulo, Brazil, in 2015. This new wave of speedcubing competitions have been and still are organised by the World Cube Association, the standard Rubiks Cube can be solved using a number of methods, not all of which are intended for speedcubing. Although some methods employ a system and algorithms, other significant methods include corners-first methods. CFOP, Roux, ZZ, and Petrus are often referred to as the big four methods, as they are the most popular, the CFOP method is considered the fastest method currently as it is has been used to set the fastest times. The CFOP method, also known as the Fridrich Method, was named one of its inventors, Jessica Fridrich. Jessica Fridrich then finished developing the method and published it online in 1997, the first step of the method is to solve a cross-shaped arrangement of edge pieces on the first layer. The remainder of the first layer and all of the layer are then solved together in what are referred to as corner-edge pairs or slots. Finally, the last layer is solved in two steps — first, all of the pieces in the layer are oriented to form a solid color and this step is referred to as orientation and is usually performed with a single set of algorithms known as OLL

11. Latin America – Latin America is a group of countries and dependencies in the Americas where Romance languages are predominant. It is therefore broader than the terms Ibero-America or Hispanic America—though it usually excludes French Canada and it has an area of approximately 19,197,000 km2, almost 13% of the Earths land surface area. As of 2015, its population was estimated at more than 626 million and in 2014, Latin America had a combined nominal GDP of 5,573,397 million USD and a GDP PPP of 7,531,585 million USD. The term Latin America was first used in 1861 in La revue des races Latines, a further investigation of the concept of Latin America is by Michel Gobat in the American Historical Review. The term was first used in Paris in an 1856 conference by the Chilean politician Francisco Bilbao and this term was also used in 1861 by French scholars in La revue des races Latines, a magazine dedicated to the Pan-Latinism movement. Latin America is, therefore, defined as all parts of the Americas that were once part of the Spanish. By this definition, Latin America is coterminous with Ibero-America and this definition emphasizes a similar socioeconomic history of the region, which was characterized by formal or informal colonialism, rather than cultural aspects. As such, some sources avoid this oversimplification by using the phrase Latin America, the distinction between Latin America and Anglo-America is a convention based on the predominant languages in the Americas by which Romance-language and English-speaking cultures are distinguished. Latin America can be subdivided into several subregions based on geography, politics, demographics and it may be subdivided on linguistic grounds into Hispanic America, Portuguese America and French America. *, Not a sovereign state The concept of Latin America has been criticized by a number of intellectuals, the earliest known settlement was identified at Monte Verde, near Puerto Montt in Southern Chile. Its occupation dates to some 14,000 years ago and there is disputed evidence of even earlier occupation. Over the course of millennia, people spread to all parts of the continents, by the first millennium CE, South Americas vast rainforests, mountains, plains and coasts were the home of tens of millions of people. Some groups formed more permanent settlements such as the Chibcha and the Tairona groups and these groups are in the circum Caribbean region. The Chibchas of Colombia, the Quechuas and Aymaras of Bolivia, the region was home to many indigenous peoples and advanced civilizations, including the Aztecs, Toltecs, Maya, and Inca. The Aztec empire was ultimately the most powerful civilization known throughout the Americas, with the arrival of the Europeans following Christopher Columbus voyages, the indigenous elites, such as the Incas and Aztecs, lost power to the heavy European invasion. Hernándo Cortés seized the Aztec elites power with the help of local groups who had favored the Aztec elite, epidemics of diseases brought by the Europeans, such as smallpox and measles, wiped out a large portion of the indigenous population. Historians cannot determine the number of natives who died due to European diseases, due to the lack of written records, specific numbers are hard to verify. Many of the survivors were forced to work in European plantations, intermixing between the indigenous peoples and the European colonists was very common, and, by the end of the colonial period, people of mixed ancestry formed majorities in several colonies

12. Feliks Zemdegs – Feliks Zemdegs is an Australian Rubiks Cube speedsolver. His surname is Latvian, and his grandparents are from Lithuania. Zemdegs bought his first speedcube in April 2008 inspired by speedcubing videos, the first unofficial time he recorded was an average of 19.73 seconds on 14 June 2008. He currently uses CFOP to solve the 3x3x3 cube, Yau method to solve the 4x4x4 cube, Zemdegs won the first competition he attended, the New Zealands Championships with an average of 13.74 seconds in the final round. He also won 2x2, 4x4, 5x5, 3x3 Blindfolded, at his next competition, the Melbourne Summer Open, Zemdegs set his first world records for 3x3x3 and 4x4x4 average, with times of 9.21 seconds and 42.01 seconds respectively. The most world records he has held at one time was after the competition in Melbourne in May 2011 where he held all 12 records listed in the first 12 columns of the table below. He won the 3x3 event at the Rubiks Cube world championship in Las Vegas in July 2013 with an average of 8.18 seconds and also came first in the 4x4 and 3x3 One handed. In addition, he won the 3x3 event at the next Rubiks Cube World Championships which took place in São Paulo in July 2015 and he also took first place in 4x4, 5x5, and 2x2. He also placed second in 6x6, 7x7, and Megaminx, the following are the official speedcubing world records set by Zemdegs that are approved by the World Cube Association.96 seconds

13. Pyraminx – The Pyraminx is a regular tetrahedron puzzle in the style of Rubiks Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubiks Cube by Erno Rubik, the Pyraminx was first conceived by Mèffert in 1970. He did nothing with his design until 1981 when he first brought it to Hong Kong for production, Uwe is fond of saying had it not been for Erno Rubiks invention of the cube, his Pyraminx would have never been produced. The Pyraminx is a puzzle in the shape of a tetrahedron, divided into 4 axial pieces,6 edge pieces. It can be twisted along its cuts to permute its pieces, the axial pieces are octahedral in shape, although this is not immediately obvious, and can only rotate around the axis they are attached to. The 6 edge pieces can be freely permuted, the trivial tips are so called because they can be twisted independently of all other pieces, making them trivial to place in solved position. Meffert also produces a similar puzzle called the Tetraminx, which is the same as the Pyraminx except that the tips are removed. The purpose of the Pyraminx is to scramble the colors, and this leaves only the 6 edge pieces as a real challenge to the puzzle. They can be solved by applying two 4-twist sequences, which are mirror-image versions of each other. These sequences permute 3 edge pieces at a time, and change their orientation differently, however, more efficient solutions are generally available. The twist of any piece is independent of the other three, as is the case with the tips. The six edges can be placed in 6. /2 positions and flipped in 25 ways, multiplying this by the 38 factor for the axial pieces gives 75,582,720 possible positions. However, setting the trivial tips to the right positions reduces the possibilities to 933,120, setting the axial pieces as well reduces the figure to only 11,520, making this a rather simple puzzle to solve. The maximum number of required to solve the Pyraminx is 11. There are 933,120 different positions, a number that is small to allow a computer search for optimal solutions.32 seconds. He also holds the fastest average of 5 with 2.14 seconds at US Nationals 2016, there are many methods for solving a Pyraminx. They can be split up into two groups, 1) V first- In these methods, two or three edges, and not a side, is solved first, and a set of algorithms, also called LL algs, are given to solve the remaining puzzle. 2) Top first methods- In these methods a block on the top, b) L4E- L4E or last 4 edges is very similar to Layer by Layer

14. Skewb Diamond – The Skewb Diamond is an octahedron-shaped puzzle similar to the Rubiks Cube. It has 14 movable pieces which can be rearranged in a total of 138,240 possible combinations and this puzzle is the dual polyhedron of the Skewb. The Skewb Diamond has 6 octahedral corner pieces and 8 triangular face centers, all pieces can move relative to each other. It is a puzzle, its planes of rotation bisect it. It is very related to the Skewb, and shares the same piece count. However, the triangular corners present on the Skewb have no visible orientation on the Skewb Diamond, combining pieces from the two can either give you an unsolvable cuboctahedron or a compound of cube and octahedron with visible orientation on all pieces. The purpose of the puzzle is to scramble its colors, the puzzle has 6 corner pieces and 8 face centers. /2. Each face center has only a single orientation, only even permutations of the corner pieces are possible, so the number of possible arrangements of corner pieces is 6. /2. Each corner has two orientations, but the orientation of the last corner is determined by the other 5. Hence, the number of possible corner orientations is 25, hence, the number of possible combinations is,4. Rubiks Cube Pyraminx Megaminx Skewb Skewb Ultimate Dogic Combination puzzles Mechanical puzzles Jaaps Skewb Diamond page

15. Dogic – The Dogic is an icosahedron-shaped puzzle like the Rubiks Cube. The 5 triangles meeting at its tips may be rotated, or 5 entire faces around the tip may be rotated and it has a total of 80 movable pieces to rearrange, compared to the 20 pieces in the Rubiks Cube. The Dogic was patented by Zoltan and Robert Vecsei in Hungary on 20 October 1993, the patent was granted 28 July 1998. In 2004, Uwe Mèffert acquired the molds from its original manufacturer at the request of puzzle fans and collectors worldwide. According to Uwe Mèffert,2000 units have been produced by him, now, the Dogics are very rare and are sold around $500 on eBay. The basic design of the Dogic is a cut into 60 triangular pieces around its 12 tips and 20 face centers. All 80 pieces can move relative to each other, there are also a good number of internal moving pieces inside the puzzle, which are necessary to keep it in one piece as its surface pieces are rearranged. There are two types of twists that it can undergo, a shallow twist which rotates the 5 triangles around a single tip, each triangle has a single color, while the face centers may have up to 3 colors, depending on the particular coloring scheme employed. The solutions for the different versions of the Dogic differ, the 12-color Dogic is the more challenging version, where the face centers must be rearranged to match the colors of the face centers in adjacent faces. The triangles must then match the colors in the face centers. The face centers are equivalent to the corner pieces of the Megaminx. The triangles are relatively easy to solve once the face centers are in place, because the 5 triangles per tip are identical in color and may be freely interchanged. The 10-color Dogic is slightly less challenging, since there is no unique solved state, the face centers may be placed relative to each other. However, it may still be desirable to put them in aesthetically pleasing arrangements, such as pairing up faces of the same color, as depicted in the second photograph. The triangles are slightly more tricky to solve than in the 12-color Dogic, because adjacent triangles in the state are not the same color. The 5-color and 2-color Dogics are even less of a challenge and these simpler versions cater to those puzzle fans who are not yet at the skill level to manage the full complexity of the 12-color Dogic. Due to different numbers of identical pieces in the two versions of the puzzle, they each have a different number of possible combinations. There are 60 tip pieces and 20 centres with 3 orientations and this limit is not reached on either puzzle, due to reducing factors detailed below

16. Combination puzzle – A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. The puzzle is solved by achieving a particular starting from a random combination. Often, the solution is required to be some recognisable pattern such as all like colours together or all numbers in order, the most famous of these puzzles is the original Rubiks Cube, a cubic puzzle in which each of the six faces can be independently rotated. Each of the six faces is a different colour, but each of the nine pieces on a face is identical in colour, in the unsolved condition colours are distributed amongst the pieces of the cube. Puzzles like the Rubiks Cube which are manipulated by rotating a layer of pieces are popularly called twisty puzzles, the mechanical construction of the puzzle will usually define the rules by which the combination of pieces can be altered. This leads to limitations on what combinations are possible. Similarly, not all the combinations that are possible from a disassembled cube are possible by manipulation of the puzzle. Since neither unpeeling the stickers nor disassembling the cube is an allowed operation, although a mechanical realization of the puzzle is usual, it is not actually necessary. It is only necessary that the rules for the operations are defined, the puzzle can be realized entirely in virtual space or as a set of mathematical statements. In fact, there are puzzles that can only be realized in virtual space. An example is the 4-dimensional 3×3×3×3 tesseract puzzle, simulated by the MagicCube4D software, there have been many different shapes of Rubik type puzzles constructed. As well as cubes, all of the regular polyhedra and many of the semi-regular, a cuboid is a rectilinear polyhedron. That is, all its edges form right angles, or in other words, a box shape. A regular cuboid, in the context of this article, is a puzzle where all the pieces are the same size in edge length. Pieces are often referred to as cubies, there are many puzzles which are mechanically identical to the regular cuboids listed above but have variations in the pattern and colour of design. Some of these are made in very small numbers, sometimes for promotional events. The ones listed in the table below are included because the pattern in some way affects the difficulty of the solution or is notable in other way. An irregular cuboid, in the context of this article, is a puzzle where not all the pieces are the same size in edge length

17. N-dimensional sequential move puzzle

On the 18th October 2015 at the Dutch Cube Day in Voorburg, Holland I was lucky enough to meet Mat Bahner and see his amazing Yottaminx puzzle. The photos and video on this page are from that day.

The Yottaminx puzzle was revealed to the world on 15th November 2014. It was designed by Matt Bahner and 3D printed by Shapeways. Matt had previously shown an Examinx Puzzle in 2011 which barely worked and unfortunately got broken. With advice from Oskar van Deventer he designed the Yottaminx puzzle you see on this page. It weighs 2kg and has 2943 parts using a similar mechanism to Oskar's Over The Top 17x17x17 Rubik's Cube puzzle. The making of this puzzle is one of the most significant achievements in the history of twisty puzzles.

To understand the significance and also it's name I need to give you a bit of history. In the 1980s puzzle manufacturer Uwe Meffert started to use the term "Pyraminx" for a number of puzzles, most of which at the time had never actually been made. There was the Pyraminx ball, Pyraminx Magic Barrel, Pyraminx Crystal and several others. This is because he was fascinated by the Egyptian pyramids and Sphinx so he combined their name. When the puzzles were actually mass produced virtually all were given new names and the "pyraminx" part was dropped. Exceptions were his famous Pyraminx plus the much later puzzle called Pyraminx Crystal. Some of the other puzzles though kept the "minx" part including the well known Megaminx.

In 2005 Tyler Fox made the world's first higher order Megaminx. Unlike a Rubik's Cube adding just one layer isn't very easy and that wasn't done until many years later on the Kilominx. For this reason Tyler added two. The name he gave it was Gigaminx. This is taken from the International System of Units which gives a standardised way of naming a mathematical series. There are several different series but the one that contains mega goes- mega, giga, tera, peta exa, etta, yotta. You may recognise these terms from computer storage. The puzzles progressed as follows-

1980s- Megaminx mass produced by Uwe Mefferts. Equivalent to 3x3x3

2005- Gigaminx prototype by Tyler Fox. Equivalent to 5x5x5.

2008- Teraminx prototype by Drewseph. Equivalent to 7x7x7.

2009- Gigaminx mass produced.

2009- Petaminx prototype by David Calzon & Flambore. Equivalent to 9x9x9.

2010- Teraminx mass produced.

2011- Examinx prototype by Matt Bahner. Equivalent to 11x11x11

2012- Petaminx mass produced.

2014- Yottaminx prototype by Matt Bahner (missing out the Zettaminx). Equivalent to 15x15x15.

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