intersphere | reciprocating sphere

The midsphere, also called the intersphere, reciprocating sphere, or inversion sphere, is a sphere with respect to which the polyhedron vertices of a polyhedron are the inversion poles of the planes of the faces of the dual polyhedron (and vice versa). The radius ρ of the midsphere is called the midradius. The midsphere touches all polyhedron edges as well as the edges of the dual of that solid Note that the midsphere does not necessarily pass through the midpoints of the edges a polyhedron dual, but is rather only tangent to the edges at some point along their lengths.

Archimedean solid | canonical polyhedron | circumsphere | dual polyhedron | insphere | inversion pole | inversion sphere | midradius | Platonic solid