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The six planes through the midpoints of the edges of a tetrahedron and perpendicular to the opposite edges concur in a point known as the Monge point.

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

Symbols used to identify irreducible representations of groups: A= singly degenerate state which is symmetric with respect to rotation about the principal C_n axis, B= singly ...

Let H be a complex Hilbert space, and define a nest as a set N of closed subspaces of H satisfying the conditions: 1. 0,H in N, 2. If N_1,N_2 in N, then either N_1 subset= ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

The Parry point is one of the two intersections of the Parry circle and the circumcircle of a triangle (the other is the focus of the Kiepert parabola, which is Kimberling ...

The pentagonal dipyramid is one of the convex deltahedra, and Johnson solid J_(13). It is also the dual polyhedron of the pentagonal prism U_(76) and is an isohedron. It is ...