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Numbers which are not perfect and for which s(N)=sigma(N)-N<N, or equivalently sigma(n)<2n, where sigma(N) is the divisor function. Deficient numbers are sometimes called ...

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 lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

Two points on a surface which are opposite to each other but not farthest from each other (e.g., the midpoints of opposite edges of a cube) are said to be transitive points. ...

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

The ditrigonal icosidodecahedral graph is the skeleton of the cube 5-compound, ditrigonal dodecadodecahedron, great ditrigonalIcosidodecahedron, and small ditrigonal ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

An imperfect graph G is a graph that is not perfect. Therefore, graphs G with omega(G)<chi(G) (1) where omega(G) is the clique number and chi(G) is the chromatic number are ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...