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An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

The cubic curve defined by ax^3+bx^2+cx+d=xy with a!=0. The curve cuts the axis in either one or three points. It was the 66th curve in Newton's classification of cubics. ...

Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation t^3+2t^2-t-1=0, (1) then the Rogers L-function satisfies L(alpha)-L(alpha^2) = 1/7 (2) ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A n-crossed prism graph for positive even n (a term introduced here for the first time), is a graph obtained by taking two disjoint cycle graphs C_n and adding edges ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...