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La kvaredro-okedra kahelaro aŭ alternita k … La kvaredro-okedra kahelaro aŭ alternita kuba kahelaro estas unuforma kahelaro de eŭklida 3-spaco. Ĝi konsistas el kvaredroj kaj okedroj. Ĝi estas ero de diversdimensia familio de alternitaj hiperkubaj kahelaroj (aŭ duonhiperkubaj kahelaroj).Ĝi estas unu el 28 konveksaj unuformaj kahelaroj de eŭklida 3-spaco. Ĝi estas vertico-transitiva kun 8 kvaredroj kaj 6 okedroj ĉirkaŭ ĉiu vertico. Ĝi estas latero-transitiva kun 2 kvaredroj kaj 2 okedroj alterne ĉirkaŭ ĉiu latero. n-dimensia alternita hiperkuba kahelaro konsistas el kaj kruco-hiperpluredraj facetoj. En ĉi tiu okazo, kvaredro estas 3-dimensia duonvertica hiperkubo kaj okedro estas 3-kruco-hiperpluredro. Kiam la kuba kahelaro estas alternita, la kubaj ĉeloj iĝas kvaredrajn ĉelojn, kaj en lokoj de la forigataj verticoj kreiĝas la novaj okedraj ĉeloj. Kiel ĉi tia, kvaredro-okedra kahelaro povas esti prezentita per etendita simbolo de Schläfli h{4,3,4} kiel enhavanta duonon de verticoj de la {4,3,4} kuba kahelaro. La simila kahelaro estas turnita kvaredro-okedra kahelaro, kiu havas najbarajn tavolojn turnitajn je 60 gradoj tiel ke duono de la lateroj estas ĉirkaŭita per du najbaraj kvaredroj kaj du najbaraj okedroj, sed ne per ili en alterna ordo.j okedroj, sed ne per ili en alterna ordo.
, The tetrahedral-octahedral honeycomb, alte … The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway calls this honeycomb a tetroctahedrille, and its dual a dodecahedrille. R. Buckminster Fuller combines the two words octahedron and tetrahedron into octet truss, a rhombohedron consisting of one octahedron (or two square pyramids) and two opposite tetrahedra. It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex. It is edge-transitive with 2 tetrahedra and 2 octahedra alternating on each edge. 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. It is part of an infinite family of uniform honeycombs called alternated hypercubic honeycombs, formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets. It is also part of another infinite family of uniform honeycombs called simplectic honeycombs. In this case of 3-space, the cubic honeycomb is alternated, reducing the cubic cells to tetrahedra, and the deleted vertices create octahedral voids. As such it can be represented by an extended Schläfli symbol h{4,3,4} as containing half the vertices of the {4,3,4} cubic honeycomb. There is a similar honeycomb called gyrated tetrahedral-octahedral honeycomb which has layers rotated 60 degrees so half the edges have neighboring rather than alternating tetrahedra and octahedra. The tetrahedral-octahedral honeycomb can have its symmetry doubled by placing tetrahedra on the octahedral cells, creating a nonuniform honeycomb consisting of tetrahedra and octahedra (as triangular antiprisms). Its vertex figure is an order-3 truncated triakis tetrahedron. This honeycomb is the dual of the triakis truncated tetrahedral honeycomb, with triakis truncated tetrahedral cells. with triakis truncated tetrahedral cells.
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La kvaredro-okedra kahelaro aŭ alternita k … La kvaredro-okedra kahelaro aŭ alternita kuba kahelaro estas unuforma kahelaro de eŭklida 3-spaco. Ĝi konsistas el kvaredroj kaj okedroj. Ĝi estas ero de diversdimensia familio de alternitaj hiperkubaj kahelaroj (aŭ duonhiperkubaj kahelaroj).Ĝi estas unu el 28 konveksaj unuformaj kahelaroj de eŭklida 3-spaco. Ĝi estas vertico-transitiva kun 8 kvaredroj kaj 6 okedroj ĉirkaŭ ĉiu vertico. Ĝi estas latero-transitiva kun 2 kvaredroj kaj 2 okedroj alterne ĉirkaŭ ĉiu latero.j kaj 2 okedroj alterne ĉirkaŭ ĉiu latero.
, The tetrahedral-octahedral honeycomb, alte … The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway calls this honeycomb a tetroctahedrille, and its dual a dodecahedrille. It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex. It is edge-transitive with 2 tetrahedra and 2 octahedra alternating on each edge. and 2 octahedra alternating on each edge.
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Kvaredro-okedra kahelaro
, Tetrahedral-octahedral honeycomb
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