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The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.
Rectified 8-cubes. In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube . There are unique 8 degrees of rectifications, the zeroth being the 8-cube, and the 7th and last being the 8-orthoplex. Vertices of the rectified 8-cube are located at the edge-centers of the 8-cube.
Runcinated 5-cubes. In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube . There are 8 unique degrees of runcinations of the 5-cube, along with permutations of truncations and cantellations. Four are more simply constructed relative to the 5-orthoplex .
In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex. There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. Half are expressed relative to the dual 6-cube.
Runcicantic 5-cube. =. Orthogonal projections in B 5 Coxeter plane. In six-dimensional geometry, a runcic 5-cube or ( runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes .
Kilburn Dam. Total capacity. 35,577,000 m 3 (28,843 acre⋅ft) Power Station. Hydraulic head. 460 m (1,510 ft) Installed capacity. 1,000 megawatts [1] The Drakensberg Pumped Storage Scheme is an energy storage facility built in the South African provinces of Free State and KwaZulu-Natal starting in 1974 and completed by 1981.
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