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dbr:List_of_geodesic_polyhedra_and_Goldberg_polyhedra
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dbr:Conway_polyhedron_notation
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dbr:Conway_ambo_operator
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dbr:Conway_bevel_operator
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dbr:Conway_dual_operator
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dbr:Conway_expand_operator
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dbr:Conway_gyro_operator
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dbr:Conway_join_operator
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dbr:Conway_meta_operator
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dbr:Conway_ortho_operator
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dbr:Conway_polyhedral_notation
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dbr:Conway_snub_operator
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dbr:Bicupola_(geometry)
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dbr:Deltoidal_hexecontahedron
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dbr:Johnson_solid
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dbr:Pentakis_icosidodecahedron
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dbr:Conway_kis_operator
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콘웨이 다면체 표기법 Notation de Conway des polyèdres Notación de poliedros de Conway Нотация Конвея для многогранников 康威多面體表示法 Pluredra skribmaniero de Conway Conway polyhedron notation
rdfs:comment
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, tC represents a truncated cube, and taC, parsed as t(aC), is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: dC = O. Applied in a series, these operators allow many to be generated. Conway defined the operators a (ambo), b (bevel), d (dual), e (expand), g (gyro), j (join), k (kis), m (meta), o (ortho), s (snub), and t (truncate), while Hart added r (ref En geometría, la notación de poliedros de Conway, inventada por John Horton Conway y promovida por George W. Hart, se usa para describir poliedros basándose en un poliedro semilla modificado mediante distintas operaciones prefijadas.​​ 콘웨이 다면체 표기법은 존 호턴 콘웨이가 개발한 다면체의 표기법이다. 기하학에서, 존 호튼 콘웨이가 발명하고 조지 W. 하트가 장려한 콘웨이 다면체 표기법은 다양한 접두사 연산에 의해 수정된 씨앗 다면체에 기초한 다면체를 묘사하기 위해 사용된다. 콘웨이와 하트는 케플러가 정의한 절단 연산자를 사용하여 동일한 대칭의 관련 다면체를 만드는 아이디어를 확장했습니다. 예를 들어 tC는 잘린 큐브를 나타내고 taC는 다음과 같이 구문 분석합니다. 다면체는 그들의 꼭짓점, 모서리, 면이 어떻게 서로 연결되는지를 위상적으로 연구하거나 공간에서의 요소 배치의 관점에서 기하학적으로 연구할 수 있습니다. 이러한 연산자의 다른 구현은 기하학적으로 다르지만 위상적으로 동일한 다면체를 생성할 수 있습니다. 이러한 위상적으로 동등한 다면체는 구에 다면체 그래프를 많이 내장하는 것으로 생각할 수 있습니다. 달리 명시되지 않은 한, 본 문서(및 Conway 연산자에 대한 일반적인 문헌)에서는 토폴로지가 주요 관심사입니다. 속이 0인 다면체는 모호함을 피하기 위해 종종 정식 형태로 놓입니다. 康威多面體表示法是用來描述多面體的一種方法。 一般是用種子多面體(seed)為基礎並標示對種子多面體做的操作或運算。 種子多面體一般都為正多面體或正多邊形密鋪,表示的字母則取他們名字的第一個字母,例如: * T = 正四面體 (Tetrahedron) * C = 正方體 (Cube) * O = 正八面體 (Octahedron) * D = 正十二面體 (Dodecahedron) * I = 正二十面體 (Icosahedron) * H = 正六邊形密鋪 (Hexagonal tiling) * Q = 正四邊形密鋪 (Quadrille = Square tiling) * Δ = 正三角形密鋪 (Deltille = Triangular tiling) 另外柱體和錐體也可以作為種子,並以它是底面邊數加一個字母表示: * P = 柱體 (Prism) * A = 反稜柱 (Antiprism) * Y = 錐體 (Pyramid) * J = 詹森多面體 (Johnson solid) 例如種子“P5”是指五角柱、“P10”是指十角柱、“Y6”是指六角錐、“J86”是指球狀屋頂、“A86”是指86角反稜柱。 任何凸多面體皆可以當作種子,前提是它可以執行操作或運算。 La notation de Conway des polyèdres est une notation des polyèdres développée par le mathématicien John Horton Conway. Elle est utilisée pour décrire des polyèdres à partir d'un polyèdre « mère » modifié par diverses opérations. Les polyèdres mères sont les solides de Platon. Нотация Конвея для многогранников, разработанная Конвеем и продвигаемая , используется для описания многогранников, опираясь на затравочный (т.е. используемый для создания других) многогранник, модифицируемый различными префикс-операциями. En geometrio, pluredra skribmaniero de Conway estas maniero por priskribi pluredrojn per vico de operacioj farataj je la fonta pluredro. La skribmaniero konsistas el la finaj signoj prezentataj la fontan pluredron kaj antaŭ ili estas signoj prezentataj la operaciojn, kiu estas aplikataj en la ordo dedekstre maldekstren. La operacioj povas generi ĉiujn arĥimedajn solidojn kaj katalanajn solidojn el la platonaj solidoj. Aplikante pli longajn seriojn de ĉi tiuj operacioj, eblas krei multajn pli malsimplajn pluredrojn.
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En geometrio, pluredra skribmaniero de Conway estas maniero por priskribi pluredrojn per vico de operacioj farataj je la fonta pluredro. La skribmaniero konsistas el la finaj signoj prezentataj la fontan pluredron kaj antaŭ ili estas signoj prezentataj la operaciojn, kiu estas aplikataj en la ordo dedekstre maldekstren. La operacioj povas generi ĉiujn arĥimedajn solidojn kaj katalanajn solidojn el la platonaj solidoj. Aplikante pli longajn seriojn de ĉi tiuj operacioj, eblas krei multajn pli malsimplajn pluredrojn. Ĝenerale ĉiu pluredro, kiu povas esti priskribita per skribmaniero de Conway, havas multajn skribmanieron. En geometría, la notación de poliedros de Conway, inventada por John Horton Conway y promovida por George W. Hart, se usa para describir poliedros basándose en un poliedro semilla modificado mediante distintas operaciones prefijadas.​​ Conway y Hart ampliaron la idea de utilizar operadores, como el truncamiento definido por Johannes Kepler, para construir poliedros relacionados con la misma simetría. Por ejemplo, tC representa un cubo truncado y taC, analizado como t(aC), es (topológicamente) un cuboctaedro truncado. El operador más simple, la conjugación intercambia elementos vértices y caras para obterner figuras duales; por ejemplo, el dual de un cubo es un octaedro: dC= O. Aplicados en serie, estos operadores permiten generar muchos poliedros de orden superior. Conway definió los operadores a (ambo), b (bisel), d (dual), e (expandir), g (giro), j (unir), k (kis), m (meta), o (orto), s (achatar) y t (truncar), mientras que Hart agregó r (reflejar) y p (hélice).​ En versiones posteriores se nombraron operadores adicionales, a veces denominados operadores extendidos.​​ Las operaciones básicas de Conway son suficientes para generar los sólidos arquimedianos y los sólidos de Catalan a partir de los sólidos platónicos. Algunas operaciones básicas se pueden realizar como compuestos de otras: por ejemplo, el ambo aplicado dos veces es la operación de expansión (aa= e), mientras que un truncamiento después del ambo produce un bisel (ta= b). Los poliedros se pueden estudiar topológicamente, en términos de cómo se conectan entre sí sus vértices, aristas y caras, o geométricamente, en términos de la ubicación de esos elementos en el espacio. Diferentes formas de estos operadores pueden generar poliedros que son geométricamente diferentes pero topológicamente equivalentes. Estos poliedros topológicamente equivalentes se pueden considerar como uno de los muchos grafos poliédricos embebidos en la esfera. A menos que se especifique lo contrario, en este artículo (y en la literatura sobre los operadores de Conway en general) la topología fija el criterio principal. Los poliedros con genus 0 (es decir, topológicamente equivalentes a una esfera) a menudo se colocan en forma canónica para evitar ambigüedades. 콘웨이 다면체 표기법은 존 호턴 콘웨이가 개발한 다면체의 표기법이다. 기하학에서, 존 호튼 콘웨이가 발명하고 조지 W. 하트가 장려한 콘웨이 다면체 표기법은 다양한 접두사 연산에 의해 수정된 씨앗 다면체에 기초한 다면체를 묘사하기 위해 사용된다. 콘웨이와 하트는 케플러가 정의한 절단 연산자를 사용하여 동일한 대칭의 관련 다면체를 만드는 아이디어를 확장했습니다. 예를 들어 tC는 잘린 큐브를 나타내고 taC는 다음과 같이 구문 분석합니다. 스타일 T(aC)를 표시합니다.}, 는 (위상적으로) 깎은 정육면체입니다. 가장 간단한 연산자 이중 꼭지점과 면 요소를 바꿉니다. 예를 들어, 이중 큐브는 8면체입니다. dC=O. 이러한 연산자는 직렬로 적용되어 많은 고차 다면체가 생성될 수 있습니다. Hart가 r과 p를 더하는 동안 Conway는 연산자 abdegjkmost를 정의했습니다. 이후 구현에서는 추가 연산자를 명명하며, 이를 "확장" 연산자라고도 합니다. 콘웨이의 기본 연산은 플라톤의 다면체에서 아르키메데스 다면체와 카탈루냐 다면체를 생성하기에 충분합니다. 예를 들어, 두 번 적용되는 앰보는 확장 연산인 aa = e인 반면, 앰보 후 잘라내면 베벨(ta = b)이 생성됩니다. 다면체는 그들의 꼭짓점, 모서리, 면이 어떻게 서로 연결되는지를 위상적으로 연구하거나 공간에서의 요소 배치의 관점에서 기하학적으로 연구할 수 있습니다. 이러한 연산자의 다른 구현은 기하학적으로 다르지만 위상적으로 동일한 다면체를 생성할 수 있습니다. 이러한 위상적으로 동등한 다면체는 구에 다면체 그래프를 많이 내장하는 것으로 생각할 수 있습니다. 달리 명시되지 않은 한, 본 문서(및 Conway 연산자에 대한 일반적인 문헌)에서는 토폴로지가 주요 관심사입니다. 속이 0인 다면체는 모호함을 피하기 위해 종종 정식 형태로 놓입니다. 康威多面體表示法是用來描述多面體的一種方法。 一般是用種子多面體(seed)為基礎並標示對種子多面體做的操作或運算。 種子多面體一般都為正多面體或正多邊形密鋪,表示的字母則取他們名字的第一個字母,例如: * T = 正四面體 (Tetrahedron) * C = 正方體 (Cube) * O = 正八面體 (Octahedron) * D = 正十二面體 (Dodecahedron) * I = 正二十面體 (Icosahedron) * H = 正六邊形密鋪 (Hexagonal tiling) * Q = 正四邊形密鋪 (Quadrille = Square tiling) * Δ = 正三角形密鋪 (Deltille = Triangular tiling) 另外柱體和錐體也可以作為種子,並以它是底面邊數加一個字母表示: * P = 柱體 (Prism) * A = 反稜柱 (Antiprism) * Y = 錐體 (Pyramid) * J = 詹森多面體 (Johnson solid) 例如種子“P5”是指五角柱、“P10”是指十角柱、“Y6”是指六角錐、“J86”是指球狀屋頂、“A86”是指86角反稜柱。 任何凸多面體皆可以當作種子,前提是它可以執行操作或運算。 何頓·康威提出這個想法, 就像克卜勒的截角定義,建立相關的多面體相同的對稱性。 它的多面體表示法能從正多面體種子表示所有阿基米德立體、半正多面體和卡塔蘭立體。 在一系列的應用中,康威多面體表示法可以產生許多高階多面體。 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, tC represents a truncated cube, and taC, parsed as t(aC), is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: dC = O. Applied in a series, these operators allow many to be generated. Conway defined the operators a (ambo), b (bevel), d (dual), e (expand), g (gyro), j (join), k (kis), m (meta), o (ortho), s (snub), and t (truncate), while Hart added r (reflect) and p (propellor). Later implementations named further operators, sometimes referred to as "extended" operators. Conway's basic operations are sufficient to generate the Archimedean and Catalan solids from the Platonic solids. Some basic operations can be made as composites of others: for instance, ambo applied twice is the expand operation (aa = e), while a truncation after ambo produces bevel (ta = b). Polyhedra can be studied topologically, in terms of how their vertices, edges, and faces connect together, or geometrically, in terms of the placement of those elements in space. Different implementations of these operators may create polyhedra that are geometrically different but topologically equivalent. These topologically equivalent polyhedra can be thought of as one of many embeddings of a polyhedral graph on the sphere. Unless otherwise specified, in this article (and in the literature on Conway operators in general) topology is the primary concern. Polyhedra with genus 0 (i.e. topologically equivalent to a sphere) are often put into canonical form to avoid ambiguity. La notation de Conway des polyèdres est une notation des polyèdres développée par le mathématicien John Horton Conway. Elle est utilisée pour décrire des polyèdres à partir d'un polyèdre « mère » modifié par diverses opérations. Les polyèdres mères sont les solides de Platon. John Conway a généralisé l'utilisation d'opérateurs, tels la (en) définie par Kepler, afin de générer d'une mère des polyèdres de même symétrie. Ses opérateurs peuvent générer des mères tous les solides d'Archimède et de Catalan. Appliqués aux séries, ces opérateurs permettent de générer une grande quantité de polyèdres d'ordres plus élevés. Нотация Конвея для многогранников, разработанная Конвеем и продвигаемая , используется для описания многогранников, опираясь на затравочный (т.е. используемый для создания других) многогранник, модифицируемый различными префикс-операциями. Конвей и Харт расширили идею использования операторов, подобных оператору truncation (усечения), определённого Кеплером, чтобы создавать связанные многогранники с той же симметрией. Базовые операторы могут сгенерировать все архимедовы тела и каталановы тела из правильных затравок. Например, tC представляет усечённый куб, а taC, полученный как t(aC), является усечённым октаэдром. Простейший оператор dual (двойственный) меняет местами вершины и грани. Так, двойственным многогранником для куба является октаэдр — dC=O. Применённые последовательно, эти операторы позволяют сгенерировать многие многогранники высокого порядка. Получающиеся многогранники будут иметь фиксированную топологию (вершины, рёбра, грани), в то время как точная геометрия не ограничивается. Затравочные многогранники, являющиеся правильными многогранниками, представляются первой буквой в их (английском) названии (Tetrahedron = тетраэдр, Octahedron = октаэдр, Cube = куб, Icosahedron = икосаэдр, Dodecahedron = додекаэдр). Кроме того, используются призмы (Pn – от prism для n-угольных призм), антипризмы (An – от Antiprisms), купола (Un – от cupolae), антикупола (Vn) и пирамиды (Yn – от pyramid). Любой многогранник может выступать в качестве затравки, если операции могут на них быть выполнены. Например, правильногранные многогранники можно обозначить как Jn (от Johnson solids = тела Джонсона) для n=1…92. В общем случае трудно предсказать результат последовательного применения двух и более операций на заданный многогранник-затравку. Например, операция ambo, применённая дважды, оказывается той же самой, что и операция expand (расширения), aa=e, в то время как операция truncation (усечение) после операции ambo даёт то же, что и операция bevel, ta=b. Не существует общей теории, описывающей, какие многогранники могут быть получены с помощью некоторого набора операторов. Наоборот, все результаты были получены эмпирически.
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dbr:Disdyakis_triacontahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Dodecahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Conway_Polyhedron_Notation
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
dbo:wikiPageRedirects
dbr:Conway_polyhedron_notation
Subject Item
dbr:Conway_notation
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Cantellation_(geometry)
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Catalan_solid
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Catmull–Clark_subdivision_surface
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Rectified_truncated_cube
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Rectified_truncated_dodecahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Rectified_truncated_icosahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Rectified_truncated_octahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Rectified_truncated_tetrahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Chamfer_(geometry)
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Snub_(geometry)
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Near-miss_Johnson_solid
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Expanded_cuboctahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Expanded_icosidodecahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Expansion_(geometry)
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:List_of_things_named_after_John_Horton_Conway
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Planigon
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Spherical_polyhedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Snub_rhombicuboctahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Pentagonal_trapezohedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Symmetrohedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Tetragonal_trapezohedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Truncated_rhombicuboctahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Trigonal_trapezohedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Truncated_triakis_icosahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Truncated_triakis_octahedron
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
Subject Item
dbr:Semikis
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
dbo:wikiPageRedirects
dbr:Conway_polyhedron_notation
Subject Item
dbr:Kis_operator
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
dbo:wikiPageRedirects
dbr:Conway_polyhedron_notation
Subject Item
dbr:Local_operations_that_preserve_orientation-preserving_symmetries
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
dbo:wikiPageRedirects
dbr:Conway_polyhedron_notation
Subject Item
dbr:Local_symmetry-preserving_operation
dbo:wikiPageWikiLink
dbr:Conway_polyhedron_notation
dbo:wikiPageRedirects
dbr:Conway_polyhedron_notation
Subject Item
wikipedia-en:Conway_polyhedron_notation
foaf:primaryTopic
dbr:Conway_polyhedron_notation