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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, 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.
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<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodecàedre"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"十二面體"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Дванадцятигранник"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dekduedro"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"黄鉄鉱体"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"五角十二面體"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodekaedro"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodécaèdre"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dvanáctistěn"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodecaedro"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Пентагондодекаэдр"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Δωδεκάεδρο"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodekaeder"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodecaedro"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodecahedron"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"اثنا عشري سطوح"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Двенадцатигранники"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"십이면체"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"十二面体"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Dodecaedro"
<http://dbpedia.org/resource/Dodecahedron>rdfs:label"Regelmatig twaalfvlak"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Das Dodekaeder [ˌdodekaˈʔeːdɐ] (von griech. Zwölfflächner; dt. auch (das) Zwölfflach) ist ein Körper mit zwölf Flächen. In der Regel ist damit ein platonischer Körper gemeint, nämlich das regelmäßige Pentagondodekaeder, ein Körper mit * 12 kongruenten regelmäßigen Fünfecken * 30 gleich langen Kanten, von denen jede die Seite von zwei Fünfecken ist * 20 Ecken, in denen jeweils drei dieser Fünfecke zusammentreffen Es gibt aber auch von hoher Symmetrie."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Дванадцятигранник (додекаедр) — многогранник з дванадцятьма гранями. Існує кілька об'ємних фігур з дванадцятьма гранями."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Dodekaeder (av grekiskans dodeka, tolv, och hedra, säte, grundyta) är en polyeder vars sidor utgörs av tolv liksidiga pentagoner. Dodekaedern är den fjärde av de fem platonska kropparna. Den har 20 tretaliga hörn och 30 kanter (att ett hörn är tretaligt betyder att det utgår tre kantlinjer från det). En regelbunden dodekaeder har Schläfli-symbolen . Den dihedrala vinkeln (vinkeln mellan två plan) är π − arctan(2), cirka 116,56°."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Dodekaedroa poliedro erregular bat da hamabi aurpegi dituena. Dodekaedroa erregularra da hamabi pentagono erregularrez osatuta dagoenean. 20 erpin, 12 aurpegi eta 30 ertz ditu."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Δωδεκάεδρο στη στερεομετρία λέγεται ένα πολύεδρο που έχει δώδεκα . Το κανονικό δωδεκάεδρο είναι ένα από τα Πλατωνικά στερεά, που έχει ως έδρες δώδεκα κανονικά πεντάγωνα, τα οποία ενώνονται ανά τρία σε κάθε κορυφή του. Ο Ευκλείδης ασχολείται με το κανονικό δωδεκάεδρο στην Πρόταση 17 του 13ου βιβλίου των Στοιχείων του (XXIII.17). Εκτός από το κανονικό δωδεκάεδρο, άλλα δωδεκάεδρα είναι το ρομβικό δωδεκάεδρο, το δεκαγωνικό πρίσμα, το πενταγωνικό αντιπρίσμα κ.ά."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Un dodecaedro (del griego δωδεκαεδρον dōdekáedron, de δώδεκα dōdeka, ‘doce’ y ἕδρα edra; ‘cara’) es un poliedro de doce caras, convexo o . Sus caras han de ser polígonos de once lados o menos. Si las doce caras del dodecaedro son pentágonos regulares, iguales entre sí, el dodecaedro es convexo y se denomina 'regular', siendo entonces uno de los llamados sólidos platónicos. Recientes investigaciones científicas han propuesto que el espacio dodecaédrico de Poincaré sería la forma del Universo​​​ y en el año 2008 se estimó la orientación óptima del modelo en el cielo.​"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"在幾何學中,五角十二面體(Pentagonal dodecahedron或Pyritohedron)是一種由12個不等邊五邊形組成的十二面體,具有四面體群對稱性。其與正十二面體類似,皆是由12個全等的五邊形組成,且每個頂點都是3個五邊形的公共頂點,但由於其面不是正多邊形,其頂點的排佈未能達到五摺對稱性,因此不屬於正多面體。部分的化學物質或礦石其晶體形狀是這種形狀,例如黄铁矿和部分的天然氣水合物。其英文名稱Pyritohedron是來自黄铁矿的英文pyrite以及多面體的字尾-hedron命名的。"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"十二面体(じゅうにめんたい、英: dodecahedron)とは、12枚の面からなる多面体である。最もよく知られる十二面体は、正多面体の一種である正十二面体である。"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"متعدد السطوح الاثنا عشري أو متعدد الأوجه الاثنا عشري (بالإنجليزية: Dodecahedron)‏ في الهندسة الرياضية عبارة عن متعدد سطوح له اثنا عشر سطحاً أو وجهاً، لكن غالبا ما يقصد به الشكل المنتظم، أي أن يكون مؤلفا من اثني عشر خماسي أضلاع."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"In geometria solida il dodecaedro è un poliedro con dodici facce. Generalmente con questo termine si intende però il dodecaedro regolare: nel dodecaedro regolare le facce sono pentagoni regolari che si incontrano in ogni vertice a gruppi di tre."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Pravidelný dvanáctistěn (dodekaedr) je trojrozměrné těleso v prostoru, jehož stěny tvoří 12 stejných pravidelných pětiúhelníků. Má 20 rohů a 30 hran. Patří mezi mnohostěny, speciálně mezi takzvaná platónská tělesa."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"黄鉄鉱体 (英:pyritohedron) は、黄鉄鉱の結晶構造にみられる十二面体の一種である。12枚の合同な四等辺五角形の面を持ち、20個の頂点にそれぞれ3本の辺が交わっている (五角十二面体の一種)。 正十二面体は、全ての面が合同な正五角形となっており、黄鉄鉱体の特殊な場合である。"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"在幾何學中,十二面體是指由十二個面組成的多面體,而由十二個全等的正五邊形組成的十二面體稱為正十二面體。 十二個面的多面體可以是正十二面體、菱形十二面體、正五角帳塔、雙四角錐柱、扭稜鍥形體、十一角錐、。"
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Un dodecàedre o dodecaedre (ambdues variants són acceptades) és un políedre regular de dotze cares. El dodecàedre és regular quan està format per dotze pentàgons regulars. Té 20 vèrtexs i 30 arestes."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Dekduedro estas iu pluredro kun 12 edroj, sed kutime estas subkomprenata la regula dekduedro kiu estas platona solido komponita el 12 du regulaj kvinlateraj edroj, el kiuj tri kuniĝas je ĉiu vertico. Ĝi havas 20 verticojn kaj 30 randojn. Ĝia estas la dudekedro."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Een regelmatig twaalfvlak, of dodecaëder, is een ruimtelijke figuur met 12 vijfhoekige vlakken, 20 hoekpunten en 30 ribben. Het is een van de vijf regelmatige veelvlakken in drie dimensies, ook platonische lichamen genoemd. Het heeft icosahedrale symmetrie. Hoewel de naam dodecaëder evenveel wordt gebruikt als regelmatig twaalfvlak, ligt het voor de duidelijkheid voor de hand over een regelmatig twaalfvlak te spreken."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Na geometria, um dodecaedro (do grego δωδεκάεδρον, doze faces) é qualquer poliedro que tenha doze faces. O mais familiar é o dodecaedro regular, um sólido platônico constituído por doze pentágonos regulares."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, 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."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Двенадцатигра́нник — многогранник с двенадцатью гранями. Существует несколько объёмных фигур с двенадцатью гранями."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"Пентаго́ндодека́эдр (от др.-греч. πενταγον — «пятиугольник» + δωδεκάεδρον — «двенадцатигранник») — объёмная фигура с двенадцатью гранями в форме неправильных пятиугольников."
<http://dbpedia.org/resource/Dodecahedron>rdfs:comment"En géométrie, un dodécaèdre est un polyèdre à douze faces. Puisque chaque face a au moins trois côtés et que chaque arête borde deux faces, un dodécaèdre a au moins 18 arêtes."
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<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/date>"October 2020"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/footer>"Orthographic projections of the pyritohedron with h = 1/2"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/footer>"Cubic and tetrahedral form"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/footer>"Natural pyrite"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/footer>"Orthographic projections from 2- and 3-fold axes"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/property/footer>"Chiral tetartoids based on the dyakis dodecahedron in the middle"
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<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"黄鉄鉱体 (英:pyritohedron) は、黄鉄鉱の結晶構造にみられる十二面体の一種である。12枚の合同な四等辺五角形の面を持ち、20個の頂点にそれぞれ3本の辺が交わっている (五角十二面体の一種)。 正十二面体は、全ての面が合同な正五角形となっており、黄鉄鉱体の特殊な場合である。"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"In geometria solida il dodecaedro è un poliedro con dodici facce. Generalmente con questo termine si intende però il dodecaedro regolare: nel dodecaedro regolare le facce sono pentagoni regolari che si incontrano in ogni vertice a gruppi di tre."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Dodekaedroa poliedro erregular bat da hamabi aurpegi dituena. Dodekaedroa erregularra da hamabi pentagono erregularrez osatuta dagoenean. 20 erpin, 12 aurpegi eta 30 ertz ditu."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"在幾何學中,五角十二面體(Pentagonal dodecahedron或Pyritohedron)是一種由12個不等邊五邊形組成的十二面體,具有四面體群對稱性。其與正十二面體類似,皆是由12個全等的五邊形組成,且每個頂點都是3個五邊形的公共頂點,但由於其面不是正多邊形,其頂點的排佈未能達到五摺對稱性,因此不屬於正多面體。部分的化學物質或礦石其晶體形狀是這種形狀,例如黄铁矿和部分的天然氣水合物。其英文名稱Pyritohedron是來自黄铁矿的英文pyrite以及多面體的字尾-hedron命名的。"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Dodekaeder (av grekiskans dodeka, tolv, och hedra, säte, grundyta) är en polyeder vars sidor utgörs av tolv liksidiga pentagoner. Dodekaedern är den fjärde av de fem platonska kropparna. Den har 20 tretaliga hörn och 30 kanter (att ett hörn är tretaligt betyder att det utgår tre kantlinjer från det). En regelbunden dodekaeder har Schläfli-symbolen . Den dihedrala vinkeln (vinkeln mellan två plan) är π − arctan(2), cirka 116,56°."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Двенадцатигра́нник — многогранник с двенадцатью гранями. Существует несколько объёмных фигур с двенадцатью гранями."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Un dodecàedre o dodecaedre (ambdues variants són acceptades) és un políedre regular de dotze cares. El dodecàedre és regular quan està format per dotze pentàgons regulars. Té 20 vèrtexs i 30 arestes."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Pravidelný dvanáctistěn (dodekaedr) je trojrozměrné těleso v prostoru, jehož stěny tvoří 12 stejných pravidelných pětiúhelníků. Má 20 rohů a 30 hran. Patří mezi mnohostěny, speciálně mezi takzvaná platónská tělesa."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Dekduedro estas iu pluredro kun 12 edroj, sed kutime estas subkomprenata la regula dekduedro kiu estas platona solido komponita el 12 du regulaj kvinlateraj edroj, el kiuj tri kuniĝas je ĉiu vertico. Ĝi havas 20 verticojn kaj 30 randojn. Ĝia estas la dudekedro."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Na geometria, um dodecaedro (do grego δωδεκάεδρον, doze faces) é qualquer poliedro que tenha doze faces. O mais familiar é o dodecaedro regular, um sólido platônico constituído por doze pentágonos regulares."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Дванадцятигранник (додекаедр) — многогранник з дванадцятьма гранями. Існує кілька об'ємних фігур з дванадцятьма гранями."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Пентаго́ндодека́эдр (от др.-греч. πενταγον — «пятиугольник» + δωδεκάεδρον — «двенадцатигранник») — объёмная фигура с двенадцатью гранями в форме неправильных пятиугольников."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"在幾何學中,十二面體是指由十二個面組成的多面體,而由十二個全等的正五邊形組成的十二面體稱為正十二面體。 十二個面的多面體可以是正十二面體、菱形十二面體、正五角帳塔、雙四角錐柱、扭稜鍥形體、十一角錐、。"
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, 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. Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular:The , a common crystal form in pyrite, has pyritohedral symmetry, while the has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling. There are numerous . While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Das Dodekaeder [ˌdodekaˈʔeːdɐ] (von griech. Zwölfflächner; dt. auch (das) Zwölfflach) ist ein Körper mit zwölf Flächen. In der Regel ist damit ein platonischer Körper gemeint, nämlich das regelmäßige Pentagondodekaeder, ein Körper mit * 12 kongruenten regelmäßigen Fünfecken * 30 gleich langen Kanten, von denen jede die Seite von zwei Fünfecken ist * 20 Ecken, in denen jeweils drei dieser Fünfecke zusammentreffen Es gibt aber auch von hoher Symmetrie."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Een regelmatig twaalfvlak, of dodecaëder, is een ruimtelijke figuur met 12 vijfhoekige vlakken, 20 hoekpunten en 30 ribben. Het is een van de vijf regelmatige veelvlakken in drie dimensies, ook platonische lichamen genoemd. Het heeft icosahedrale symmetrie. Hoewel de naam dodecaëder evenveel wordt gebruikt als regelmatig twaalfvlak, ligt het voor de duidelijkheid voor de hand over een regelmatig twaalfvlak te spreken."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"متعدد السطوح الاثنا عشري أو متعدد الأوجه الاثنا عشري (بالإنجليزية: Dodecahedron)‏ في الهندسة الرياضية عبارة عن متعدد سطوح له اثنا عشر سطحاً أو وجهاً، لكن غالبا ما يقصد به الشكل المنتظم، أي أن يكون مؤلفا من اثني عشر خماسي أضلاع."
<http://dbpedia.org/resource/Dodecahedron><http://dbpedia.org/ontology/abstract>"Un dodecaedro (del griego δωδεκαεδρον dōdekáedron, de δώδεκα dōdeka, ‘doce’ y ἕδρα edra; ‘cara’) es un poliedro de doce caras, convexo o . Sus caras han de ser polígonos de once lados o menos. Si las doce caras del dodecaedro son pentágonos regulares, iguales entre sí, el dodecaedro es convexo y se denomina 'regular', siendo entonces uno de los llamados sólidos platónicos. Recientes investigaciones científicas han propuesto que el espacio dodecaédrico de Poincaré sería la forma del Universo​​​ y en el año 2008 se estimó la orientación óptima del modelo en el cielo.​"
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