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An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

The polyhedron compound of the truncated dodecahedron and its dual, the triakis icosahedron. The compound can be constructed from a truncated dodecahedron of unit edge length ...

The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...