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The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

The diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(76). This solid is the diminished polyhedron obtained by diminishing a small ...

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...

The polyhedron compound of the icosahedron (U_(22)) and the great dodecahedron (U_(35)), sometimes known as the small cid. Four faces meet at each edge of the small complex ...

The largest area of intersection of a solid body by a plane parallel to a given plane, also called the "HA measurement."

The mean tangent diameter of a solid, also known as the mean caliper diameter, is the caliper dimension obtained by averaging over all orientations.