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Let a cone of opening parameter c and vertex at (0,0,0) intersect a sphere of radius r centered at (x_0,y_0,z_0), with the cone oriented such that its axis does not pass ...

There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was ...

There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and ...

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

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

The "echidnahedron" is the term for the spiky fourth icosahedron stellation (in the enumeration of Maeder 1994) apparently first used in the Netlib polyhedron database. It is ...

The Engel polyhedra are two 38-faced plesiohedra (and hence space-filling) discovered by Engel (Engel 1981; Engel 1986, p. 220; Grünbaum and Shephard 1980; Senechal 1990, ...

A golden isozonohedron is a zonohedron all of whose faces are golden rhombi. There exist exactly five golden isozonohedra, as summarized in the following table. face count ...

A polyhedron compound of the great icosahedron and its dual great stellated dodecahedron most easily constructed by adding the polyhedron vertices of the former to the latter.