. . . . "In mathematics, a convex body in -dimensional Euclidean space is a compact convex set with non-empty interior. A convex body is called symmetric if it is centrally symmetric with respect to the origin; that is to say, a point lies in if and only if its antipode, also lies in Symmetric convex bodies are in a one-to-one correspondence with the unit balls of norms on Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope."@en . "In mathematics, a convex body in -dimensional Euclidean space is a compact convex set with non-empty interior. A convex body is called symmetric if it is centrally symmetric with respect to the origin; that is to say, a point lies in if and only if its antipode, also lies in Symmetric convex bodies are in a one-to-one correspondence with the unit balls of norms on Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope."@en . "En matem\u00E1tica, un cuerpo convexo n-dimensi\u00F3nal en un espacio Eucl\u00EDdeo Rn es un conjunto convexo compacto con un interior no vac\u00EDo. Un cuerpo convexo K es llamado sim\u00E9trico si este es centralmente sim\u00E9trico con respecto al origen, por ejemplo, un punto x se encuentra en K si y solo si su , \u2212x, tambi\u00E9n se encuentra en K. Los cuerpos convexos sim\u00E9tricos est\u00E1n en una correspondencia uno-a-uno con las bolas unidad de normas sobre Rn. Importantes ejemplos de cuerpos convexos son la bola eucl\u00EDdea, el hipercubo y el politopo de cruce."@es . . "Convex body"@en . . . . "En matem\u00E1tica, un cuerpo convexo n-dimensi\u00F3nal en un espacio Eucl\u00EDdeo Rn es un conjunto convexo compacto con un interior no vac\u00EDo. Un cuerpo convexo K es llamado sim\u00E9trico si este es centralmente sim\u00E9trico con respecto al origen, por ejemplo, un punto x se encuentra en K si y solo si su , \u2212x, tambi\u00E9n se encuentra en K. Los cuerpos convexos sim\u00E9tricos est\u00E1n en una correspondencia uno-a-uno con las bolas unidad de normas sobre Rn. Importantes ejemplos de cuerpos convexos son la bola eucl\u00EDdea, el hipercubo y el politopo de cruce."@es . . "Konvexer K\u00F6rper"@de . "In matematica, un corpo convesso in uno spazio euclideo n-dimensionale \u00E8 un insieme convesso compatto con parte interna non vuota. Un corpo convesso K \u00E8 detto \"simmetrico\" se presenta una simmetria centrale rispetto all'origine, ossia un punto x giace in K se e solo se il suo antipodo, \u2212x, giace anch'esso in K. I corpi convessi simmetrici sono in corrispondenza biunivoca con le sfere unitarie per le norme in Rn. Esempi importanti di corpi convessi sono la palla euclidea, l'ipercubo e il ."@it . . . "1333"^^ . "8652020"^^ . "Corpo convesso"@it . "Ein konvexer K\u00F6rper ist in der Mathematik ein geometrischer K\u00F6rper, der konvex ist und dessen Inhalt nicht leer ist."@de . . . . . . . . . . . . "\u6570\u5B66\u4E2D\uFF0C\u5728n-\u7EF4\u6B27\u6C0F\u7A7A\u95F4Rn\u7684\u51F8\u4F53\uFF08\u82F1\u8A9E\uFF1AConvex body\uFF09\u662F\u4E00\u4E2A\u5185\u90E8\u975E\u7A7A\u7684\u7D27\u51F8\u96C6\u3002 \u5982\u679C\u51F8\u4F53K\u662F\u5173\u4E8E\u4E2D\u5FC3\u70B9\u5BF9\u79F0\u7684\u5BF9\u79F0\u51F8\u4F53\uFF0C\u5373\u5BF9K\u7684\u4EFB\u4E00\u70B9x\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u7684\u6709\u5BF9\u4E2D\u5FC3\u70B9\u5BF9\u79F0\u70B9-x\u4E5F\u5728\u51F8\u4F53K\u4E0A\u3002\u663E\u7136\u5BF9\u79F0\u51F8\u4F53K\u548CRn\u7A7A\u95F4\u4E0A\u5355\u4F4D\u7403\u5728\u7BC4\u4E0A\u4E00\u4E00\u5BF9\u5E94\u3002 \u51F8\u4F53\u7684\u91CD\u8981\u7684\u4F8B\u5B50\u662F\u6B27\u51E0\u91CC\u5F97\u7403\uFF0C\u7ACB\u65B9\u4F53\u548C\u4EA4\u53C9\u591A\u9762\u4F53\u3002"@zh . . "\u6570\u5B66\u4E2D\uFF0C\u5728n-\u7EF4\u6B27\u6C0F\u7A7A\u95F4Rn\u7684\u51F8\u4F53\uFF08\u82F1\u8A9E\uFF1AConvex body\uFF09\u662F\u4E00\u4E2A\u5185\u90E8\u975E\u7A7A\u7684\u7D27\u51F8\u96C6\u3002 \u5982\u679C\u51F8\u4F53K\u662F\u5173\u4E8E\u4E2D\u5FC3\u70B9\u5BF9\u79F0\u7684\u5BF9\u79F0\u51F8\u4F53\uFF0C\u5373\u5BF9K\u7684\u4EFB\u4E00\u70B9x\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u7684\u6709\u5BF9\u4E2D\u5FC3\u70B9\u5BF9\u79F0\u70B9-x\u4E5F\u5728\u51F8\u4F53K\u4E0A\u3002\u663E\u7136\u5BF9\u79F0\u51F8\u4F53K\u548CRn\u7A7A\u95F4\u4E0A\u5355\u4F4D\u7403\u5728\u7BC4\u4E0A\u4E00\u4E00\u5BF9\u5E94\u3002 \u51F8\u4F53\u7684\u91CD\u8981\u7684\u4F8B\u5B50\u662F\u6B27\u51E0\u91CC\u5F97\u7403\uFF0C\u7ACB\u65B9\u4F53\u548C\u4EA4\u53C9\u591A\u9762\u4F53\u3002"@zh . . "Ein konvexer K\u00F6rper ist in der Mathematik ein geometrischer K\u00F6rper, der konvex ist und dessen Inhalt nicht leer ist."@de . "1087932095"^^ . . . . . . . . . "\u51F8\u4F53"@zh . "In matematica, un corpo convesso in uno spazio euclideo n-dimensionale \u00E8 un insieme convesso compatto con parte interna non vuota. Un corpo convesso K \u00E8 detto \"simmetrico\" se presenta una simmetria centrale rispetto all'origine, ossia un punto x giace in K se e solo se il suo antipodo, \u2212x, giace anch'esso in K. I corpi convessi simmetrici sono in corrispondenza biunivoca con le sfere unitarie per le norme in Rn. Esempi importanti di corpi convessi sono la palla euclidea, l'ipercubo e il ."@it . . . "Cuerpo convexo"@es .