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The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...

The trivial group, denoted E or <e>, sometimes also called the identity group, is the unique (up to isomorphism) group containing exactly one element e, the identity element. ...

A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

An ascending chain of subspaces of a vector space. If V is an n-dimensional vector space, a flag of V is a filtration V_0 subset V_1 subset ... subset V_r, (1) where all ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

The Yff contact triangle DeltaX_AX_BX_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_(190). It is the polar triangle of the Yff ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...