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Hexagonal Trapezohedron
In geometry, a hexagonal trapezohedron or deltohedron is the fourth in an infinite series of trapezohedra which are dual polyhedra to the antiprisms. It has twelve faces which are congruent kites. It can be described by the Conway notationbr> It is an isohedral (face-transitive) figure, meaning that all its faces are the same. More specifically, all faces are not merely congruent but also ''transitive'', i.e. lie within the same '' symmetry orbit''. Convex isohedral polyhedra are the shapes that will make fair dice. Symmetry The symmetry a hexagonal trapezohedron is D6d of order 24. The rotation group is D6 of order 12. Variations One degree of freedom within D6 symmetry changes the kites into congruent quadrilaterals with 3 edges lengths. In the limit, one edge of each quadrilateral goes to zero length, and these become bipyramids. Crystal arrangements of atoms can repeat in space with hexagonal trapezohedral cells. If the kites surrounding the two peaks are of differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezohedra
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, or -deltohedron is the dual polyhedron of an antiprism. The faces of an are congruent and symmetrically staggered; they are called ''twisted kites''. With a higher symmetry, its faces are ''kites'' (also called ''trapezoids'', or ''deltoids''). The "" part of the name does not refer to faces here, but to two arrangements of each vertices around an axis of symmetry. The dual antiprism has two actual faces. An trapezohedron can be dissected into two equal pyramids and an antiprism. Terminology These figures, sometimes called deltohedra, must not be confused with deltahedra, whose faces are equilateral triangles. ''Twisted'' ''trigonal'', ''tetragonal'', and ''hexagonal trapezohedra'' (with six, eight, and twelve ''twisted'' congruent kite faces) exist as crystals; in crystallography (describing the crystal habits of minerals), they are just called ''trigonal'', ''tetragonal'', and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezohedron
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, or -deltohedron is the dual polyhedron of an antiprism. The faces of an are congruent and symmetrically staggered; they are called ''twisted kites''. With a higher symmetry, its faces are ''kites'' (also called ''trapezoids'', or ''deltoids''). The "" part of the name does not refer to faces here, but to two arrangements of each vertices around an axis of symmetry. The dual antiprism has two actual faces. An trapezohedron can be dissected into two equal pyramids and an antiprism. Terminology These figures, sometimes called deltohedra, must not be confused with deltahedra, whose faces are equilateral triangles. ''Twisted'' ''trigonal'', ''tetragonal'', and ''hexagonal trapezohedra'' (with six, eight, and twelve ''twisted'' congruent kite faces) exist as crystals; in crystallography (describing the crystal habits of minerals), they are just called ''trigonal'', ''tetragonal'', and ''he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipyramid
A (symmetric) -gonal bipyramid or dipyramid is a polyhedron formed by joining an -gonal pyramid and its mirror image base-to-base. An -gonal bipyramid has triangle faces, edges, and vertices. The "-gonal" in the name of a bipyramid does not refer to a face but to the internal polygon base, lying in the mirror plane that connects the two pyramid halves. (If it were a face, then each of its edges would connect three faces instead of two.) "Regular", right bipyramids A ''"regular"'' bipyramid has a ''regular'' polygon base. It is usually implied to be also a ''right'' bipyramid. A ''right'' bipyramid has its two apices ''right'' above and ''right'' below the center or the ''centroid'' of its polygon base. A "regular" right (symmetric) -gonal bipyramid has Schläfli symbol . A right (symmetric) bipyramid has Schläfli symbol , for polygon base . The "regular" right (thus face-transitive) -gonal bipyramid with regular vertices is the dual of the -gonal uniform (thus right) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Hexagonal Trapezohedron
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. 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 centre of the sphere, and 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 object 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 the sphere's r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Tiling
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. Much of the theory of symmetrical polyhedra is most conveniently derived in this way. The most familiar spherical polyhedron is the soccer ball, thought of as a spherical truncated icosahedron. The next most popular spherical polyhedron is the beach ball, thought of as a hosohedron. Some "improper" polyhedra, such as hosohedra and their duals, dihedra, exist as spherical polyhedra, but their flat-faced analogs are degenerate. The example hexagonal beach ball, is a hosohedron, and is its dual dihedron. History The first known man-made polyhedra are spherical polyhedra carved in stone. Many have been found in Scotland, and appear to date from the neolithic period (the New Stone Age). During the 10th Century, the Islamic scholar Abū al-Wafā' Būzjānī (Abu'l Wafa) wrote the first ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unequal Twisted Hexagonal Trapezohedron Net
Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * Spatial inequality, the unequal distribution of income and resources across geographical regions * Income inequality metrics, used to measure income and economic inequality among participants in a particular economy * International inequality, economic differences between countries Healthcare * Health equity, the study of differences in the quality of health and healthcare across different populations Mathematics * Inequality (mathematics), a relation between two values when they are different Social sciences * Educational inequality, the unequal distribution of academic resources to socially excluded communities * Gender inequality, unequal treatment or perceptions of individuals due to their gender * Participation inequality, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unequal Hexagonal Trapezohedron Net
Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * Spatial inequality, the unequal distribution of income and resources across geographical regions * Income inequality metrics, used to measure income and economic inequality among participants in a particular economy * International inequality, economic differences between countries Healthcare * Health equity, the study of differences in the quality of health and healthcare across different populations Mathematics * Inequality (mathematics), a relation between two values when they are different Social sciences * Educational inequality, the unequal distribution of academic resources to socially excluded communities * Gender inequality, unequal treatment or perceptions of individuals due to their gender * Participation inequality, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twisted Hexagonal Trapezohedron2 Net
Twisted may refer to: Film and television * ''Twisted'' (1986 film), a horror film by Adam Holender starring Christian Slater * ''Twisted'' (1996 film), a modern retelling of ''Oliver Twist'' * ''Twisted'', a 2011 Singapore Chinese film directed by Chai Yee Wei * ''Twisted'' (2004 film), a thriller starring Ashley Judd and Andy Garcia * ''Twisted'', a parody musical by StarKid Productions * ''Twisted'' (TV series), 2013 * "Twisted" (''Star Trek: Voyager''), a television episode * ''Twisted'' (web series), an Indian erotic thriller web series Software and games * '' Twisted: The Game Show'', a 1994 3DO game * Twisted (software), an event-driven networking framework * '' WarioWare: Twisted!'', a 2005 game for the Game Boy Advance Books * ''Twisted'' (book), a short story collection by crime writer Jeffery Deaver ** '' More Twisted'', a second short story collection by Deaver * ''Twisted'', a novel by Laurie Halse Anderson * ''Twisted'', a ''Pretty Little Liars'' novel by Sar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twisted Hexagonal Trapezohedron Net
Twisted may refer to: Film and television * ''Twisted'' (1986 film), a horror film by Adam Holender starring Christian Slater * ''Twisted'' (1996 film), a modern retelling of ''Oliver Twist'' * ''Twisted'', a 2011 Singapore Chinese film directed by Chai Yee Wei * ''Twisted'' (2004 film), a thriller starring Ashley Judd and Andy Garcia * ''Twisted'', a parody musical by StarKid Productions * ''Twisted'' (TV series), 2013 * "Twisted" (''Star Trek: Voyager''), a television episode * ''Twisted'' (web series), an Indian erotic thriller web series Software and games * '' Twisted: The Game Show'', a 1994 3DO game * Twisted (software), an event-driven networking framework * '' WarioWare: Twisted!'', a 2005 game for the Game Boy Advance Books * ''Twisted'' (book), a short story collection by crime writer Jeffery Deaver ** '' More Twisted'', a second short story collection by Deaver * ''Twisted'', a novel by Laurie Halse Anderson * ''Twisted'', a ''Pretty Little Liars'' novel by Sar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unequal Twisted Hexagonal Trapezohedron
Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * Spatial inequality, the unequal distribution of income and resources across geographical regions * Income inequality metrics, used to measure income and economic inequality among participants in a particular economy * International inequality, economic differences between countries Healthcare * Health equity, the study of differences in the quality of health and healthcare across different populations Mathematics * Inequality (mathematics), a relation between two values when they are different Social sciences * Educational inequality, the unequal distribution of academic resources to socially excluded communities * Gender inequality, unequal treatment or perceptions of individuals due to their gender * Participation inequality, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unequal Hexagonal Trapezohedron
Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * Spatial inequality, the unequal distribution of income and resources across geographical regions * Income inequality metrics, used to measure income and economic inequality among participants in a particular economy * International inequality, economic differences between countries Healthcare * Health equity, the study of differences in the quality of health and healthcare across different populations Mathematics * Inequality (mathematics), a relation between two values when they are different Social sciences * Educational inequality, the unequal distribution of academic resources to socially excluded communities * Gender inequality, unequal treatment or perceptions of individuals due to their gender * Participation inequality, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twisted Hexagonal Trapezohedron2
Twisted may refer to: Film and television * ''Twisted'' (1986 film), a horror film by Adam Holender starring Christian Slater * ''Twisted'' (1996 film), a modern retelling of ''Oliver Twist'' * ''Twisted'', a 2011 Singapore Chinese film directed by Chai Yee Wei * ''Twisted'' (2004 film), a thriller starring Ashley Judd and Andy Garcia * ''Twisted'', a parody musical by StarKid Productions * ''Twisted'' (TV series), 2013 * "Twisted" (''Star Trek: Voyager''), a television episode * ''Twisted'' (web series), an Indian erotic thriller web series Software and games * '' Twisted: The Game Show'', a 1994 3DO game * Twisted (software), an event-driven networking framework * '' WarioWare: Twisted!'', a 2005 game for the Game Boy Advance Books * ''Twisted'' (book), a short story collection by crime writer Jeffery Deaver ** '' More Twisted'', a second short story collection by Deaver * ''Twisted'', a novel by Laurie Halse Anderson * ''Twisted'', a ''Pretty Little Liars'' novel by Sar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
