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Pentakis Dodecahedron
In geometry, a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron; that is, it is the Kleetope of the dodecahedron. Specifically, the term typically refers to a particular Catalan solid, namely the Dual polyhedron, dual of a truncated icosahedron. Cartesian coordinates Let \phi be the golden ratio. The 12 points given by (0, \pm 1, \pm \phi) and cyclic permutations of these coordinates are the vertices of a regular icosahedron. Its dual regular dodecahedron, whose edges intersect those of the icosahedron at right angles, has as vertices the points (\pm 1, \pm 1, \pm 1) together with the points (\pm\phi, \pm 1/\phi, 0) and cyclic permutations of these coordinates. Multiplying all coordinates of the icosahedron by a factor of (3\phi+12)/19\approx 0.887\,057\,998\,22 gives a slightly smaller icosahedron. The 12 vertices of this icosahedron, together with the vertices of the dodecahedron, are the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Dodecahedron T01 H3
Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual number, a number system used in automatic differentiation * Dual (grammatical number), a grammatical category used in some languages * Dual county, a Gaelic games county which competes in both Gaelic football and hurling * Dual diagnosis, a psychiatric diagnosis of co-occurrence of substance abuse and a mental problem * Dual fertilization, simultaneous application of a P-type and N-type fertilizer * Dual impedance, electrical circuits that are the dual of each other * Dual SIM cellphone supporting use of two SIMs * Aerochute International Dual a two-seat Australian powered parachute design Acronyms and other uses * Dual (brand), a manufacturer of Hifi equipment * DUAL (cognitive architecture), an artificial intelligence design model * DUAL algorithm, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Atomic
''Doctor Atomic'' is an opera by the contemporary American composer John Adams, with a libretto by Peter Sellars. It premiered at the San Francisco Opera on October 1, 2005. The work focuses on how leading figures at Los Alamos dealt with the great stress and anxiety of preparing for the test of the first atomic bomb (the "Trinity" test). In 2007, a documentary was made by Jon H. Else about the creation of the opera and collaboration between Adams and Sellars, titled ''Wonders Are Many''. Composition history The first act takes place about a month before the bomb is to be tested, and the second act is set in the early morning of July 16, 1945 (the day of the test). During the second act, time is shown slowing down for the characters and then snapping back to the clock. The opera ends in the final, prolonged moment before the bomb is detonated. Although the original commission for the opera suggested that U.S. physicist J. Robert Oppenheimer, the "father of the atomic bomb", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Crystal Maze
''The Crystal Maze'' is a British game show devised by Jacques Antoine, based upon his format for the French game show '' Fort Boyard'', and produced for Channel 4. The programme focuses on teams of contestants, a mixed group of men and women, attempting a range of challenges to earn time required to help them complete one final challenge, which if completed successfully earns them a prize. The premise of the show is themed around challenges set to different periods of human history within a fictional labyrinth of time and space (the titular "Crystal Maze"), and is notable for the use of golf ball-sized Swarovski glass crystals (referred to as "time crystals") as a reward for each challenge successfully completed by contestants, and lock-in conditions for contestants that ran out of time or broke a three-strikes rule on a challenge. ''The Crystal Maze'' originally consisted of six series, including five Christmas specials involving teams of children, which aired between 15 Feb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walt Disney World
The Walt Disney World Resort is an destination resort, entertainment resort complex located about southwest of Orlando, Florida, United States. Opened on October 1, 1971, the resort is operated by Disney Experiences, a division of the Walt Disney Company. The property covers nearly , of which half has been developed. Walt Disney World contains numerous recreational facilities designed to attract visitors for an extended stay, including four theme parks, two water parks, four golf courses, conference centers, a competitive sports complex and a shopping, dining and entertainment complex. Additionally, there are 19 Disney-owned resort hotels and one camping resort on the property, and many other non-Disney-operated resorts on and near the property. Designed to supplement Disneyland in Anaheim, California, which had opened in 1955, the complex was developed by Walt Disney in the 1960s. Walt wanted to build a new park because Disneyland in California was limited from expanding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spaceship Earth (Disney)
Spaceship Earth is a dark ride attraction at the EPCOT theme park at the Walt Disney World in Bay Lake, Florida. The geodesic sphere in which the attraction is housed has served as the symbolic structure of EPCOT since the park opened in 1982. The 15-minute ride takes guests on a time machine-themed experience, demonstrating how advancements in human communication have helped to create the future one step at a time. Riding in Omnimover-type vehicles along a track that spirals up and down the geodesic sphere, passengers are taken through scenes depicting important breakthroughs in communication throughout history—from the development of early language through cave paintings, to the use of hieroglyphs, to the invention of the alphabet, to the creation of the printing press, to today's modern communication advancements, including telecommunication, mass communication, and the internet. An opening day attraction, the ride has been updated three times—in 1986, 1994, and 2007 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excavated Dodecahedron
In geometry, the excavated dodecahedron is a star polyhedron that looks like a regular dodecahedron, dodecahedron with concave pentagonal pyramids in place of its faces. Its exterior surface represents the The Fifty Nine Icosahedra, Ef1g1 stellation of the icosahedron. It appears in Magnus Wenninger's book ''Polyhedron Models'' as model 28, the ''third stellation of icosahedron''. Description All 20 vertices and 30 of its 60 edges belong to its regular dodecahedron, dodecahedral hull. The 30 other internal edges are longer and belong to a great stellated dodecahedron. (Each contains one of the 30 edges of the regular icosahedron, icosahedral core.) Each face is a List of self-intersecting polygons, self-intersecting hexagon with alternating long and short edges and 60° angles. The equilateral triangles touching a short edge are part of the face. (The smaller one between the long edges is a face of the icosahedral core.) Faceting of the dodecahedron It has the same external for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Pentakis Dodecahedron
A sphere (from Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ''center'' of the sphere, and the distance is the sphere's ''radius''. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings. Basic terminology As mentioned earlier is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schlegel Diagram
In geometry, a Schlegel diagram is a projection of a polytope from \mathbb^d into \mathbb^ through a point just outside one of its facets. The resulting entity is a polytopal subdivision of the facet in \mathbb^ that, together with the original facet, is combinatorially equivalent to the original polytope. The diagram is named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimension 3, a Schlegel diagram is a projection of a polyhedron into a plane figure; in dimension 4, it is a projection of a 4-polytope to 3-space. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes. Construction The most elementary Schlegel diagram, that of a polyhedron, was described by Duncan Sommerville as follows: :A very useful method of representing a convex polyhedron is by plane projection. If it is projected from any external point, since each ray cuts it twice, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deltahedron
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. Deltahedra can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral triangles. There are eight convex deltahedra, which can be used in the applications of chemistry as in the polyhedral skeletal electron pair theory and chemical compounds. There are infinitely many concave deltahedra. Strictly convex deltahedron A polyhedron is said to be ''convex'' if a line between any two of its vertices lies either within its interior or on its boundary, and additionally, if no two faces are coplanar (lying in the same plane) and no two edges are collinear (segments of the same line), it can be considered as being strictly convex. Of the eight convex deltahedra, three are Platonic solids and five are Johnson solids. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others''Mathematical Programming'', by Melvyn W. Jeter (1986) p. 68/ref> (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts identify a convex polytope with its boundary. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. In the influential textbooks of Grünbaum and Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
