- 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...
- 'inspheres' of
their polyhedra. Cir****scribed
sphere Inscribed circle Midsphere Sphere ****ng Coxeter, H.S.M.
Regular Polytopes 3rd Edn.
Dover (1973)...
- 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....
-
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...
- polygon#Regular polygons. The same can be said of a
regular polyhedron's insphere,
midsphere and cir****sphere. 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...
- r_{\mathrm {i} }={\frac {\sqrt {6}}{3}}a\approx 0.817a,} the
radius of its
midsphere is: OEIS: A179587) r m = 2 2 3 a ≈ 0.943 a , {\displaystyle r_{\mathrm...
