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The 14-faced Archimedean solid with faces 8{3}+6{8}. It is also the uniform polyhedron with Maeder index 9 (Maeder 1997), Wenninger index 8 (Wenninger 1989), Coxeter index 21 ...

The truncated dodecahedron is the 32-faced Archimedean solid with faces 20{3}+12{10}. It is also uniform polyhedron with Maeder index 26 (Maeder 1997), Wenninger index 10 ...

Minkowski's conjecture states that every lattice tiling of R^n by unit hypercubes contains two hypercubes that meet in an (n-1)-dimensional face. Minkowski first considered ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian ...

The area of the shadow of a body on a plane, also called the "outer quermass."

The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

The evolute of a circle is a degenerate point at the origin.

The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...