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The truncated dodecahedron is the 32-faced Archimedean solid with faces 20{3}+12{10}. It is also uniform polyhedron with Maeder index 26 (Maeder 1997), Wenninger index 10 ...

The truncated tetrahedron is the Archimedean solid with faces 4{3}+4{6}. It is also the uniform polyhedron with Maeder index 2 (Maeder 1997), Wenninger index 6 (Wenninger ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body B with volume V is not known. If B is a parallelepiped, then the smallest-volume ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...