Noun
intersphere (plural interspheres)
English Wikipedia has an article on:intersphereWikipedia
(geometry) A sphere that is tangent to every edge of a given polyhedron.
If we reciprocate such a polyhedron about its intersphere, the dual polyhedron will share the same edge-tangency points and so must also be canonical; it is the canonical dual, and the two together form a canonical dual pair. Source: Internet
In this example the size of the vertex figure was chosen so that its circumcircle lies on the intersphere of the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron. Source: Internet