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The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

The dihedral group D_n is the symmetry group of an n-sided regular polygon for n>1. The group order of D_n is 2n. Dihedral groups D_n are non-Abelian permutation groups for ...

The great dodecahedron is the Kepler-Poinsot polyhedron whose dual is the small stellated dodecahedron. It is also uniform polyhedron with Maeder index 35 (Maeder 1997), ...

The stella octangula is a polyhedron compound composed of a tetrahedron and its dual (a second tetrahedron rotated 180 degrees with respect to the first). The stella ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron of unit edge length by ...

Am octagonal prims is a prism composed of octagonal faces. The regular right octagonal prism of unit edge length has surface area and volume S = 4(3+sqrt(2)) (1) V = ...

The polyhedron compound of the small rhombicuboctahedron and its dual, the deltoidal icositetrahedron. The compound can be constructed from a small rhombicuboctahedron of ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...