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In geometry, a cube [a] is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross. [1] The cube is the only regular hexahedron and is one of the five Platonic solids.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right angles .
Four-dimensional space ( 4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
Cuboid. In geometry, a cuboid is a quadrilateral -faced convex hexahedron (a polyhedron with six faces). "Cuboid" means "like a cube ", in the sense of a convex solid which can be transformed into a cube by adjusting the lengths of its edges or/and the angles between its adjacent faces. In general mathematical language, a cuboid is a convex ...
Impossible cube. Viewed from a certain angle, this cube appears to defy the laws of geometry. The impossible cube or irrational cube is an impossible object invented by M.C. Escher for his print Belvedere. It is a two-dimensional figure that superficially resembles a perspective drawing of a three-dimensional cube, with its features drawn ...
Catalan solid. A toroidal polyhedron. In geometry, a polyhedron ( pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many', and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices . A convex polyhedron is a polyhedron that bounds a convex set.
The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. [1] It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side.
Properties. convex, isogonal regular, Hanner polytope. In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces . It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .
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