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Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Snub icosidodecahedron. Two chiral copies of the snub cube, as alternated (red or green) vertices of the truncated cuboctahedron. A snub cube can be constructed from a rhombicuboctahedron by rotating the 6 blue square faces until the 12 white square faces become pairs of equilateral triangle faces. In geometry, a snub is an operation applied to ...
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
The snub cube is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [6] It is chiral, meaning there are two distinct forms whenever being mirrored. Therefore, the snub cube has the rotational octahedral symmetry.
Menger sponge. An illustration of M4, the sponge after four iterations of the construction process. In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) [1][2][3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two ...
Constructible number. The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length can be constructed with compass and ...
The dual of a cube is an octahedron.Vertices of one correspond to faces of the other, and edges correspond to each other. In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. [1]
A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat reflective surfaces. It reflects waves incident from any direction directly towards the source, but translated. The three intersecting surfaces often have square shapes. Radar corner reflectors made of metal are used to reflect radio waves from ...