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A vertex configuration can also be represented as a polygonal vertex figure showing the faces around the vertex. This vertex figure has a 3-dimensional structure since the faces are not in the same plane for polyhedra, but for vertex-uniform polyhedra all the neighboring vertices are in the same plane and so this plane projection can be used to visually represent the vertex configuration.
A configuration, also called an instantaneous description (ID), is a finite representation of the machine at a given time. For example, for a finite automata and a given input, the configuration will be the current state and the number of read letters, for a Turing machine it will be the state, the content of the tape and the position of the head.
In network science, the Configuration Model is a family of random graph models designed to generate networks from a given degree sequence. Unlike simpler models such as the Erdős–Rényi model, Configuration Models preserve the degree of each vertex as a pre-defined property. This flexibility allows the modeler to construct networks with ...
The Archimedean solids have a single vertex configuration and highly symmetric properties. A vertex configuration indicates which regular polygons meet at each vertex. For instance, the configuration indicates a polyhedron in which each vertex is met by alternating two triangles and two pentagons.
The configuration matrix is a matrix in which the rows and columns correspond to the elements of a polyhedron as in the vertices, edges, and faces. The diagonal of a matrix denotes the number of each element that appears in a polyhedron, whereas the non-diagonal of a matrix denotes the number of the column's elements that occur in or at the row ...
For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re-added ...
The value is the energy associated with vertex configuration number . One aims to calculate the partition function of an ... of ice is given by the formula
In the Thomson problem, concerning the minimum-energy configuration of charged particles on a sphere, and for the Tammes problem of constructing a spherical code maximizing the smallest distance among the points, the minimum solution known for = places the points at the vertices of a regular icosahedron, inscribed in a sphere. This ...