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Pentakis Snub Dodecahedron
The pentakis snub dodecahedron is a convex polyhedron with 140 triangular faces, 210 edges, and 72 vertices. It has chiral icosahedral symmetry. Spherical Models, IV. Geodesic domes, p.83 Photo 36,2,1 Construction It comes from a topological construction from the snub dodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the faces are computed to be the same distance from the center. 80 of the triangles are equilateral, and 60 triangles from the pentagons are isosceles. It is a (2,1) geodesic polyhedron, made of all triangles. The path between the valence-5 vertices is two edges in a row, and then a turn and one more edge. See also * Tetrakis snub cubebr>k4sC References * John H. Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English people, English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Polyhedron K5sI
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrakis Snub Cube , a convex polyhedron with 32 faces
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Tetrakis may refer to: *Tetrakis (Paphlagonia), an ancient Greek city *Tetrakis cuboctahedron, convex polyhedron with 32 triangular faces * Tetrakis hexahedron, an Archimedean dual solid or a Catalan solid * Tetrakis square tiling, a tiling of the Euclidean plane See also *Tetracus *Tetrakis legomenon, a word that occurs only four times within a context *Tetricus (other) *Tetrix (other) *Truncated tetrakis cube The truncated tetrakis cube, or more precisely an order-6 truncated tetrakis cube or hexatruncated tetrakis cube, is a convex polyhedron with 32 faces: 24 sets of 3 bilateral symmetry pentagons arranged in an octahedral arrangement, with 8 regular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic Polyhedron
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra with mostly hexagonal faces. Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts. The most well-known may be the geodesic domes designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra. The capsids of some viruses have the shape of geodesic polyhedra, and fullerene molecules have the shape of Goldberg polyhedra. Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution of vertices than the UV sphere. The Goldberg–Coxeter construction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Kis Operator
In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations. Conway and Hart extended the idea of using operators, like truncation as defined by Kepler, to build related polyhedra of the same symmetry. For example, represents a truncated cube, and , parsed as , is ( topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: . Applied in a series, these operators allow many higher order polyhedra to be generated. Conway defined the operators (ambo), ( bevel), ( dual), (expand), (gyro), (join), (kis), (meta), (ortho), (snub), and (truncate), while Hart added ( reflect) and (propellor). Later implementations named further operators, sometimes referred to as "extended" operators. Conway's basic operations are sufficient to generate the Archimedean and C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snub Dodecahedron
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. It has two distinct forms, which are mirror images (or " enantiomorphs") of each other. The union of both forms is a compound of two snub dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron. Kepler first named it in Latin as dodecahedron simum in 1619 in his Harmonices Mundi. H. S. M. Coxeter, noting it could be derived equally from either the dodecahedron or the icosahedron, called it snub icosidodecahedron, with a vertical extended Schläfli symbol s \scriptstyle\begin 5 \\ 3 \end and flat Schläfli symbol sr. Cartesian coordinates Let ''ξ'' ≈ be the real zero of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosahedral Symmetry
In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection), for a total symmetry order of 120. The full symmetry group is the Coxeter group of type . It may be represented by Coxeter notation and Coxeter diagram . The set of rotational symmetries forms a subgroup that is isomorphic to the alternating group on 5 letters. Description Icosahedral symmetry is a mathematical property of objects indicating that an object has the same symmetries as a regular icosahedron. As point group Apart from the two infinite series of prismatic and antiprismatic symmetry, rotati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex (geometry)
In geometry, a vertex (in plural form: vertices or vertexes) is a point (geometry), point where two or more curves, line (geometry), lines, or edge (geometry), edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedron, polyhedra are vertices. Definition Of an angle The ''vertex'' of an angle is the point where two Line (mathematics)#Ray, rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments, and lines that result in two straight "sides" meeting at one place. :(3 vols.): (vol. 1), (vol. 2), (vol. 3). Of a polytope A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection (Euclidean geometry), intersection of Edge (geometry), edges, face (geometry), faces or facets of the object. In a polygon, a vertex is called "convex set, convex" if the internal an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal. Relation to edges in graphs In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment. However, any polyhedron can be represented by its skeleton or edge-skeleton, a graph whose vertices are the geometric vertices of the polyhedron and whose edges correspond to the geometric edges. Conversely, the graphs that are skeletons of three-dimensional polyhedra can be characterized by Steinitz's theore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Face (geometry)
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a ''polyhedron''. In more technical treatments of the geometry of polyhedra and higher-dimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).. Polygonal face In elementary geometry, a face is a polygon on the boundary of a polyhedron. Other names for a polygonal face include polyhedron side and Euclidean plane ''tile''. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope. With this meaning, the 4-dimensional tesseract has 24 square faces, each sharing two of 8 cubic cells. Number of polygonal faces of a polyhedron Any convex polyhedron's surface has Euler characteristic :V - E + F = 2, where ''V'' is the number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
