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A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...

A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n = CCub_n+6P_(n-1)^((4)) (1) = (2n-1)(2n^2-2n+1), (2) where ...

The set of all planes through a line. The line is sometimes called the axis of the sheaf, and the sheaf itself is sometimes called a pencil (Altshiller-Court 1979, p. 12; ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other (Steinhaus ...

A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

The supersphere is the algebraic surface that is the special case of the superellipse with a=b=c. It has equation |x/a|^n+|y/a|^n+|z/a|^n=1 (1) or |x|^n+|y|^n+|z|^n=a^n (2) ...