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Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

A number of attractive cube 10-compounds can be constructed. The first can be obtained by beginning with an initial cube and rotating it by an angle theta=sin^(-1)(sqrt(3/8)) ...

"Jabulani polyhedron" is a term introduced here to refer to the polyhedron illustrated above which underlies the shape of the soccer ball used in the 2010 World Cup in South ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...