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The Doyle graph, sometimes also known as the Holt graph (Marušič et al. 2005), is the quartic symmetric graph on 27 nodes illustrated above in several embeddings. It is ...

For a finite group G, let p(G) be the subgroup generated by all the Sylow p-subgroups of G. If X is a projective curve in characteristic p>0, and if x_0, ..., x_t are points ...

A B-spline is a generalization of the Bézier curve. Let a vector known as the knot vector be defined T={t_0,t_1,...,t_m}, (1) where T is a nondecreasing sequence with t_i in ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

Consider a quadratic equation x^2-sx+p=0 where s and p denote signed lengths. The circle which has the points A=(0,1) and B=(s,p) as a diameter is then called the Carlyle ...

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle. Its trilinear vertex matrix is ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...