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The skeleton graphs of the Johnson solids are polyhedral graphs. The Johnson skeleton graphs J_3 and J_(63) are minimal unit-distance forbidden graphs. The skeleton of the ...

A dipyramid, also called a bipyramid, consists of two pyramids symmetrically placed base-to-base. The dipyramids are duals of the regular prisms. Their skeletons are the ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...

The equilateral elongated square dipyramid, illustrated above together with its net, is Johnson solid J_(15). A version of the elongated square dipyramid that is "squashed" ...

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

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

Neville's algorithm is an interpolation algorithm which proceeds by first fitting a polynomial of degree 0 through the point (x_k,y_k) for k=1, ..., n, i.e., P_k(x)=y_k. A ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...