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A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

Let psi = 1+phi (1) = 1/2(3+sqrt(5)) (2) = 2.618033... (3) (OEIS A104457), where phi is the golden ratio, and alpha = lnphi (4) = 0.4812118 (5) (OEIS A002390). Define the ...

The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

When the elongated square pyramid with unit edge lengths (i.e., an equilateral obelisk) is truncated by a plane passing through opposite corners of its square base and the ...

A heptahedron is a polyhedron with seven faces. Because there are 34 heptahedral graphs, there are 34 topologically distinct convex heptahedra. There are three semiregular ...

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

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 ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...