The centers in the circumscribed and inscribed spheres coincide with the centroid of the disphenoid.

In contrast, there exist polyhedra that do not have an equivalent form with an inscribed sphere or circumscribed sphere.

Failing that a circumscribed sphere, inscribed sphere, or midsphere (one with all edges as tangents) can be used.

The icosahedron has the largest number of faces, the largest dihedral angle, and it hugs its inscribed sphere the tightest.

In the regular polyhedra, the inscribed sphere, midsphere, and circumscribed sphere all exist and are concentric.

We also have that a tetrahedron is a disphenoid if and only if the center in the circumscribed sphere and the inscribed sphere coincide.

It is expressed as the ratio of the average radius of curvature of the edges or corners to the radius of curvature of the maximum inscribed sphere.

The midsphere is so-called because it is between the inscribed sphere (which is tangent to every face of a polyhedron) and the circumscribed sphere (which touches every vertex).

In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

All regular polyhedra have inscribed spheres, but most irregular polyhedra do not have all facets tangent to a common sphere, although it is still possible to define the largest contained sphere for such shapes.

In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 4:3.

If the edge length of a rhombic triacontahedron is a, surface area, volume, the radius of an inscribed sphere (tangent to each of the rhombic triacontahedron's faces) and midradius, which touches the middle of each edge are:

A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side of the outer figure (but see Inscribed sphere for semantic variants).

Alexandria covered two-thirds of the second chamber floor, thirty-one-hundred square kilometers of glorious white and gold and bronze and green towers arrayed in spirals and stepped ranks, walls of blunt-faced black and gold cubes, ornately inscribed spheres rising from massive cradles themselves rich with colors and populations.