The first exotic spheres were constructed by John Milnor in the case n = 7. They were S3-bundles over S4. This type of exotic sphere is called a Milnor sphere. Later techniques based on algebraic topology enable calculations of the numbers of distinct exotic spheres, in a given dimension. For dimension 7, there are 28 or 15 depending on whether the differential equivalence includes orientation or not.
Quartz sphere are composed of minerals and the colour of the sphere is determined by the element that the mineral was fused upon during their formation under the earth.
While there are many exotic mineralized crystal available for sale in the market, few comes in spherical form as they are either too small to be polished, break easily during polish or too expensive for design such as gems.
Spheres sold in shop here are normally AA, A, B and C. Grading is determine by clarify, colour and minimal crack or inclusion; not to confused with hair like crystalline in spheres of phantoms.
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