About: Parallelohedron

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In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron.

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  • In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. (en)
  • Параллелоэдр ― выпуклый многогранник, параллельным перенесением которого можно замостить пространство, то есть покрыть евклидово пространство так, чтобы многогранники не входили друг в друга и не оставляли пустот между собой . (ru)
  • 在幾何學中，平行多面體是一種特殊的面可遞多面體，可以僅透過平移來使多面體可以面與面重疊，不同於一般的面可遞多面體，一般常見的面可遞多面體可能還要藉由旋轉或鏡射才能面與面重疊。 平行多面體除了有每面全等的特性外，也有相對面互相平行的特性。這種特性使得平行多面體可以獨立密鋪三維空間。平行多面體只能由平行四邊形面、對邊互相平行的六邊形面或其他平行多邊形面構成。平行多面體可以視為平行多邊形在三維空間的類比。 平行多面體共有5種類型，最早是由在他的晶體學系統研究中給出定義。 (zh)
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  • ly (en)
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  • October 2020 (en)
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  • Primary parallelohedron (en)
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  • PrimaryParallelohedron (en)
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  • In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. (en)
  • Параллелоэдр ― выпуклый многогранник, параллельным перенесением которого можно замостить пространство, то есть покрыть евклидово пространство так, чтобы многогранники не входили друг в друга и не оставляли пустот между собой . (ru)
  • 在幾何學中，平行多面體是一種特殊的面可遞多面體，可以僅透過平移來使多面體可以面與面重疊，不同於一般的面可遞多面體，一般常見的面可遞多面體可能還要藉由旋轉或鏡射才能面與面重疊。 平行多面體除了有每面全等的特性外，也有相對面互相平行的特性。這種特性使得平行多面體可以獨立密鋪三維空間。平行多面體只能由平行四邊形面、對邊互相平行的六邊形面或其他平行多邊形面構成。平行多面體可以視為平行多邊形在三維空間的類比。 平行多面體共有5種類型，最早是由在他的晶體學系統研究中給出定義。 (zh)
rdfs:label
  • Parallelohedron (en)
  • Параллелоэдр (ru)
  • 平行多面體 (zh)
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