Midsphere

Article summary

on the sphere.|alt=An opaque white polyhedron with four triangular faces and four quadrilateral faces is crossed by a transparent blue sphere of approximately the same size, tangent to each edge of the polyhedron. The visible portions of the sphere, outside the polyhedron, form circular caps on each face of the polyhedron, of two sizes: smaller in the triangular faces, and larger in the quadrilateral faces. Red circles on the surface of the sphere, passing through these caps, mark the horizons visible from each polyhedron vertex. The red circles have the same two sizes as the circular caps: smaller circles surround the polyhedron vertices where three faces meet, and larger circles surround the vertices where four faces meet. In geometry, 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 the uniform polyhedra, including the regular, quasiregular and semiregular polyhedra and their duals (Catalan solids) all have midspheres. The radius of the midsphere is called the midradius. A polyhedron that has a midsphere is said to be midscribed about this sphere.…

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