The Radius of the Midsphere of a Polyhedron, also called the Interradius. For a Regular
Polyhedron with Schläfli Symbol , the Dual Polyhedron is . Denote
the Inradius , midradius , and Circumradius , and let the side length be . Then

(1) | |||

(2) |

For Regular Polyhedra and Uniform Polyhedra, the Dual Polyhedron has Circumradius and Inradius . Let be the Angle subtended by the Edge of an Archimedean Solid. Then

(3) | |||

(4) | |||

(5) |

so

(6) |

(7) |

for an Archimedean Solid.

**References**

Cundy, H. and Rollett, A. *Mathematical Models, 3rd ed.* Stradbroke, England: Tarquin Pub., pp. 126-127, 1989.

© 1996-9

1999-05-26