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The Danzer graph is the Levi graph of the Danzer configuration (Boben et al. 2015). It has 70 vertices and 140 edges and is quartic, bipartite, self-dual, and unit-distance. ...

The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

There are at least two graphs associated with H. Walther. A graph on 25 vertices which appears somewhat similar to Tutte's fragment is implemented without discussion or ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

A finite group is a group having finite group order. Examples of finite groups are the modulo multiplication groups, point groups, cyclic groups, dihedral groups, symmetric ...