the midsphere or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but...

that, for a polyhedron with a circumscribed sphere, inscribed sphere, or midsphere (one with all edges as tangents), this can be used. However, it is possible...

'inspheres' of their polyhedra. Circumscribed sphere Inscribed circle Midsphere Sphere packing Coxeter, H.S.M. Regular Polytopes 3rd Edn. Dover (1973)...

graph of a convex polyhedron all of whose edges are tangent to a common midsphere. An undirected graph is a system of vertices and edges, each edge connecting...

time. Other spheres defined for some but not all polyhedra include a midsphere, a sphere tangent to all edges of a polyhedron, and an inscribed sphere...

graph and that has a midsphere, a sphere tangent to all of the edges of the polyhedron. Conversely, if a polyhedron has a midsphere, then the circles formed...

^{\ast }\rho .} Dualizing with respect to the midsphere (d = ρ) is often convenient because the midsphere has the same relationship to both polyhedra....

polygon#Regular polygons. The same can be said of a regular polyhedron's insphere, midsphere and circumsphere. The region of the plane between two concentric circles...

is a sphere that contains the polyhedron and touches every vertex. The midsphere of a convex polyhedron is a sphere tangent to every edge. Therefore, given...

their centroids, with radius 1 2 a {\textstyle {\frac {1}{2}}a} . The midsphere of a cube is the sphere tangent to the edges of a cube, with radius 1...