MIDSPHERE

In geometry, the 'midsphere' or 'intersphere' of a polyhedron is a sphere which is tangent to every edge of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere.
The radius of this sphere is called the midradius.
Important classes of polyhedra which have interspheres include:

★ Canonical polyhedra. These have the unit sphere for their midsphere, i.e. midradius = 1.

★ The Uniform polyhedra, including the regular, quasiregular and semiregular polyhedra and their duals.
Where the dual polyhedron is also considered, for example in constructing a dual compound, the intersphere is commonly used as the reciprocating sphere. When a canonical polyhedron is dualised in this way, the 'canonical dual' is obtained.
It can also be convenient to use it as an inversion sphere.

Contents

See also

References

External links

See also

★ Inscribed sphere

★ Circumscribed sphere

References

★ Coxeter, H.S.M. ''Regular Polytopes'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

★ Cundy, H.M. and Rollett, A.P. ''Mathematical Models'', OUP (Second Edition 1961).

★ Hart, G. Calculating canonical polyhedra, ''Mathematica in Education and Research'' '6', Issue 3 (1997), pp 5-10.

External links

★