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In hyperbolic geometry, the order-5 dodeca … In hyperbolic geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {5,3,5}, it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is an icosahedron. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space.rm a uniform honeycomb in spherical space.
, En geometrio, la ordo-5 dekduedra kahelaro … En geometrio, la ordo-5 dekduedra kahelaro estas unu el kvar kahelaroj de hiperbola 3-spaco. Estas kvin dekduedroj ĉirkaŭ ĉiu latero, kaj 20 dekduedroj ĉirkaŭ ĉiu vertico. La duedra angulo de dekduedro en eŭklida spaco estas ~116,6°, tiel neeblas kunigi kvin dekduedrojn ĉirkaŭ latero en eŭklida 3-spaco. Tamen en hiperbola spaco, sufiĉe grandaj dekduedroj povas havi duedraj anguloj je akurate 72 gradoj, tiel kvin de ili bone kuniĝas ĉirkaŭ latero. Estas ankaŭ la alia regula kahelaro en hiperbola 3-spaco kun dekduedraj ĉeloj, la ordo-4 dekduedra kahelaro kiu havas 4 dekduedrojn ĉirkaŭ ĉiu latero.Ĉi tiuj kahelaroj estas similaj ankaŭ al la 120-ĉelo kiu povas esti konsiderata kiel kahelaro de 3-sfero (surfaco en 4-dimensia eŭklida spaco), kun 3 dekduedroj ĉirkaŭ ĉiu latero. La dutranĉita formo de ĉi tiu kahelaro, t1,2{5,3,5}, havas ĉiuj senpintigitaj dudekedraj ĉeloj.havas ĉiuj senpintigitaj dudekedraj ĉeloj.
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In hyperbolic geometry, the order-5 dodeca … In hyperbolic geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {5,3,5}, it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is an icosahedron. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. tessellation in any number of dimensions.
, En geometrio, la ordo-5 dekduedra kahelaro … En geometrio, la ordo-5 dekduedra kahelaro estas unu el kvar kahelaroj de hiperbola 3-spaco. Estas kvin dekduedroj ĉirkaŭ ĉiu latero, kaj 20 dekduedroj ĉirkaŭ ĉiu vertico. La duedra angulo de dekduedro en eŭklida spaco estas ~116,6°, tiel neeblas kunigi kvin dekduedrojn ĉirkaŭ latero en eŭklida 3-spaco. Tamen en hiperbola spaco, sufiĉe grandaj dekduedroj povas havi duedraj anguloj je akurate 72 gradoj, tiel kvin de ili bone kuniĝas ĉirkaŭ latero. La dutranĉita formo de ĉi tiu kahelaro, t1,2{5,3,5}, havas ĉiuj senpintigitaj dudekedraj ĉeloj.havas ĉiuj senpintigitaj dudekedraj ĉeloj.
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| rdfs:label |
Ordo-5 dekduedra kahelaro
, Order-5 dodecahedral honeycomb
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