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An n-he (a term coined by Brendan Owen) is a shape formed from a polyhex by removing half of each hexagon in such a way that the remaining pieces are connected (Clarke). The ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

A generalization of the polyominoes using a collection of equal-sized equilateral triangles (instead of squares) arranged with coincident sides. Polyiamonds are sometimes ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in ...

Let f(z) = z+a_1+a_2z^(-1)+a_3z^(-2)+... (1) = zsum_(n=0)^(infty)a_nz^(-n) (2) = zg(1/z) (3) be a Laurent polynomial with a_0=1. Then the Faber polynomial P_m(f) in f(z) of ...