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The pentagonal icositetrahedron is the 24-faced dual polyhedron of the snub cube A_7 and Wenninger dual W_(17). The mineral cuprite (Cu_2O) forms in pentagonal ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

The circum-orthic triangle DeltaA^'B^'C^' is the circumcevian triangle of a triangle DeltaABC with respect to the orthocenter H (Kimberling 1998, p. 163). The circum-orthic ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

The ampersand curve is the name given by Cundy and Rowlett (1989, p. 72) to the quartic curve with implicit equation (y^2-x^2)(x-1)(2x-3)=4(x^2+y^2-2x)^2. (1) Although it is ...