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In mathematics, 6-sphere coordinates are a coordinate system for three-dimensional space obtained by inverting the 3D Cartesian coordinates across the unit 2-sphere + + =.They are so named because the loci where one coordinate is constant form spheres tangent to the origin from one of six sides (depending on which coordinate is held constant and whether its value is positive or negative).
One example is the surface of the 6-sphere, S 6. This is the set of all points in seven-dimensional space (Euclidean) that are a fixed distance from the origin. This constraint reduces the number of coordinates needed to describe a point on the 6-sphere by one, so it has six dimensions.
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere [a] or the n-dimensional surface of higher dimensional spheres.
The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition a sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical ...
Six spheres surround an octahedral voids with three spheres coming from one layer and three spheres coming from the next layer. Structures of many simple chemical compounds, for instance, are often described in terms of small atoms occupying tetrahedral or octahedral holes in closed-packed systems that are formed from larger atoms.
This is the annular Soddy's hexlet (Figure 2). Six spheres s 1 –s 6 may be packed around c and likewise sandwiched between the bounding planes a and b. Re-inversion restores the three original spheres, and transforms s 1 –s 6 into a hexlet for the original problem. In general, these hexlet spheres S 1 –S 6 have different radii.
Nutritionists reveal the 6 best different kinds of salt, when you should be using them, and how much salt you should be consuming in a day.
Packings where all spheres are constrained by their neighbours to stay in one location are called rigid or jammed. The strictly jammed (mechanically stable even as a finite system) regular sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only π √ 2 /9 ≈ 0.49365. [6]