midsphere

noun4

1. •
   A middle sphere or region.

   • For rescue or personnel-transfer purposes, the midsphere could also, like DSRV, be equipped with a transfer bell. — 1968
2. •
   A supposed realm between earth and heaven.

   • This celestial river (Nadī) transforms into [the] terrestrial one (sindhu) after falling from heaven (midsphere) in the form of rain-drops. — 2003
3. •
   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).
4. •
   The sphere, between two given spheres, by which each of the latter may be inverted into the other.