- 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 cir****scribed sphere,
inscribed sphere, or
midsphere (one with all
edges as tangents), this can be used. However, it is possible...
-
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....
-
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...
- 'inspheres' of
their polyhedra. Cir****scribed
sphere Inscribed circle Midsphere Sphere ****ng Coxeter, H.S.M.
Regular Polytopes 3rd Edn.
Dover (1973)...
-
respect to the
midsphere of C{\displaystyle {\bf {C}}}. Then A{\displaystyle {\bf {A}}} is an
Archimedean solid with the same
midsphere.
Denote the length...
- {\displaystyle r={\frac {1}{3}}R={\frac {a}{\sqrt {24}}}\,}
Radius of
midsphere that is
tangent to
edges r M = r R = a 8 {\displaystyle r_{\mathrm {M}...
- 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...
- is a
sphere that
contains the
polyhedron and
touches every edge. The
midsphere of a
convex polyhedron is a
sphere tangent to its
every edge. Therefore...
