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The polyhedron compound of the truncated dodecahedron and its dual, the triakis icosahedron. The compound can be constructed from a truncated dodecahedron of unit edge length ...

The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length ...

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

An undecahedron is a polyhedron having 11 faces. Examples include those illustrated above and summarized in the following table. F E V name 11 8 17 biaugmented triangular ...

The series sum_(j=1)^(infty)f_j(z) is said to be uniformly Cauchy on compact sets if, for each compact K subset= U and each epsilon>0, there exists an N>0 such that for all ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

A triple integral over three coordinates giving the volume within some region G, V=intintint_(G)dxdydz.

int_0^(pi/2)cos^nxdx = int_0^(pi/2)sin^nxdx (1) = (sqrt(pi)Gamma(1/2(n+1)))/(nGamma(1/2n)) (2) = ((n-1)!!)/(n!!){1/2pi for n=2, 4, ...; 1 for n=3, 5, ..., (3) where Gamma(n) ...

An open three-manifold which is simply connected but is topologically distinct from Euclidean three-space.

Two patterns T_1 and T_2 belong to the same Wilf class if |S_n(T_1)|=|S_n(T_2)| for all n, where S_n(T) denotes the set of permutations on {1,...,n} that avoid the pattern T. ...