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The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

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

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...

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 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 polyhedron compound of the truncated octahedron and its dual, the tetrakis hexahedron. The compound can be constructed from a truncated octahedron of unit edge length by ...

A generalization of a solid such as a cube or a sphere to more than three dimensions. A four-dimensional version of a polyhedron is known as a polytope.

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

The numbers lambda_(nun) in the Gaussian quadrature formula Q_n(f)=sum_(nu=1)^nlambda_(nun)f(x_(nun)).