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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 ...

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol {5,3,3}. It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

The first (called the "Blanuša double" by Orbanić et al. 2004) and second (called the "Blanuša snark" by Orbanić et al. 2004) Blanuša snarks were the second and third snarks ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

A convex polyomino (sometimes called a "convex polygon") is a polyomino whose perimeter is equal to that of its minimal bounding box (Bousquet-Mélou et al. 1999). ...

A digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...