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Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

A map projection in which areas on a sphere, and the areas of any features contained on it, are mapped to the plane in such a way that two are related by a constant scaling ...

A topologically invariant property of a surface defined as the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it. ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

Some elements of a group G acting on a space X may fix a point x. These group elements form a subgroup called the isotropy group, defined by G_x={g in G:gx=x}. For example, ...

The level set of a differentiable function f:R^n->R corresponding to a real value c is the set of points {(x_1,...,x_n) in R^n:f(x_1,...,x_n)=c}. For example, the level set ...

An auxiliary latitude which gives a sphere having correct distances along the meridians. It is denoted mu (or omega) and is given by mu=(piM)/(2M_p). (1) M_p is evaluated for ...

The Schwarz triangles are spherical triangles which, by repeated reflection in their indices, lead to a set of congruent spherical triangles covering the sphere a finite ...