midsphere

Etymology
From.

Noun

 * 1) A middle sphere or region.
 * 2)  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).
 * 3)  The sphere, between two given spheres, by which each of the latter may be inverted into the other.
 * 4) * 1994, Tim Gallagher, Bruce Piper, Chapter 7: Convexity Preserving Surface Interpolation, Nickolas S. Sapidis, Designing Fair Curves and Surfaces, page 179,
 * For any two circles (spheres) there always exists at least one midcircle (midsphere) which inverts the two given circles (spheres) into each other. in the older literature this is also known as the circle (sphere) of antisimilitude.The center of a midcircle (midsphere) is the center of similitude of two given circles (spheres).Clearly the midcircle (midsphere) of two equal circles (spheres) is the midline (midplane) between the two, which is partial justification for calling inversion in a circle or sphere reflection in a circle or sphere.
 * 1)  A supposed realm between earth and heaven.
 * 1)  The sphere, between two given spheres, by which each of the latter may be inverted into the other.
 * 2) * 1994, Tim Gallagher, Bruce Piper, Chapter 7: Convexity Preserving Surface Interpolation, Nickolas S. Sapidis, Designing Fair Curves and Surfaces, page 179,
 * For any two circles (spheres) there always exists at least one midcircle (midsphere) which inverts the two given circles (spheres) into each other. in the older literature this is also known as the circle (sphere) of antisimilitude.The center of a midcircle (midsphere) is the center of similitude of two given circles (spheres).Clearly the midcircle (midsphere) of two equal circles (spheres) is the midline (midplane) between the two, which is partial justification for calling inversion in a circle or sphere reflection in a circle or sphere.
 * 1)  A supposed realm between earth and heaven.
 * 1)  A supposed realm between earth and heaven.