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For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

The Heawood graph is a cubic graph on 14 vertices and 21 edges which is the unique (3,6)-cage graph. It is also a Moore graph. It has graph diameter 3, graph radius 3, and ...

An algebraic surface of surface order 4. Unlike cubic surfaces, quartic surfaces have not been fully classified. Examples of quartic surfaces include the apple surface, ...

The nth cubic number n^3 is a sum of n consecutive odd numbers, for example 1^3 = 1 (1) 2^3 = 3+5 (2) 3^3 = 7+9+11 (3) 4^3 = 13+15+17+19, (4) etc. This identity follows from ...

A generalized hexagon is a generalized polygon of order 6. GH(1,2) is more commonly known as the Heawood graph, but is also the (3,6)-cage graph, the cubic vertex-transitive ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

Let a tree S be a subgraph of a cubic graph G. The graph excision G circleminus S is the graph resulting from removing the tree, then merging the edges. For example, if in ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...