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The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

The azimuthal angle is an angle measured from the x-axis in the xy-plane in spherical coordinates, denoted theta in this work.

The use of coordinates (such as Cartesian coordinates) in the study of geometry. Cartesian geometry is named after René Descartes (Bell 1986, p. 48), although Descartes may ...

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The zenith angle is an angle measured from the z-axis in spherical coordinates, denoted phi in this work. It is also known as the polar angle and colatitude.

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

A reference triangle is a triangle relative to which trilinear coordinates, exact trilinear coordinates, derived triangle, or other objects are defined in triangle geometry ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...