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There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

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 ...