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If F is a group, then the extensions G of F of order o with G/phi(G)=F, where phi(G) is the Frattini subgroup, are called Frattini extensions.

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

The gabled rhombohedra are a family of elongated gyrobifastigium that are space-filling. The equilateral elongated gyrobifastigium, illustrated above, is one such example.

The dual of the great ditrigonal dodecicosidodecahedron U_(42) and Wenninger dual W_(81).

A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.

The hacoversine, also known as the hacoversed sine and cohaversine, is a little-used trigonometric function defined by hacoversin(z) = coversinz (1) = 1/2(1-sinz), (2) where ...

A pyramid with a heptagonal base. The heptagonal pyramid is one of the 257 convex octahedra.

A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.

The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...