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There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The operator norm of a linear operator T:V->W is the largest value by which T stretches an element of V, ||T||=sup_(||v||=1)||T(v)||. (1) It is necessary for V and W to be ...

A number of graphs are associated with P. J. Owens. The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It ...

The parabiaugmented hexagonal prism is a convex equilateral solid that is Johnson solid J_(56). The parabiaugmented hexagonal prism has volume V=1/6(2sqrt(2)+9sqrt(3)) (1) ...

The parabiaugmented truncated dodecahedron is a convex equilateral solid that is Johnson solid J_(69). The unit parabiaugmented truncated dodecahedron has volume ...

The parabididiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(820). The unit parabididiminished rhombicosidodecahedron ...

The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small rhombicosidodecahedron located in the ...

The paragyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(77). The unit paragyrate diminished rhombicosidodecahedron has volume ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...