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In a given triangle DeltaABC with all angles less than 120 degrees (2pi/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point," Torricelli point, or ...

The great stellated dodecahedron is one of the Kepler-Poinsot polyhedra. It is also the uniform polyhedron with Maeder index 52 (Maeder 1997), Wenninger index 22 (Wenninger ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

Regge calculus is a finite element method utilized in numerical relativity in attempts of describing spacetimes with few or no symmetries by way of producing numerical ...

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...