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A closed three-dimensional figure (which may, according to some terminology conventions, be self-intersecting). Kern and Bland (1948, p. 18) define a solid as any limited ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

The thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...