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The great dodecahedron is the Kepler-Poinsot polyhedron whose dual is the small stellated dodecahedron. It is also uniform polyhedron with Maeder index 35 (Maeder 1997), ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

An n-Hadamard graph is a graph on 4n vertices defined in terms of a Hadamard matrix H_n=(h)_(ij) as follows. Define 4n symbols r_i^+, r_i^-, c_i^+, and c_i^-, where r stands ...

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...

Let the sum of the squares of the digits of a positive integer s_0 be represented by s_1. In a similar way, let the sum of the squares of the digits of s_1 be represented by ...

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance to a schematic illustration of a house ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...