Definitions from Wiktionary (midsphere)

▸ noun:  A middle sphere or region.
▸ noun:  (geometry, solid geometry) The sphere which, if it exists, is tangent to every edge of a given polyhedron and with respect to which the polyhedron's vertices are the inversion poles of the planes of the faces of its dual polyhedron (and vice versa).
▸ noun:  (geometry) The sphere, between two given spheres, by which each of the latter may be inverted into the other.
▸ noun:  (religion, Vedic mythology, uncountable) A supposed realm between earth and heaven.



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