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The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the z-axis is the axis about which the ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the other with widths of convex domains (Bang 1951). The theorem of Bang (1897) states that ...

A system of circles obtained by multiplying each radius in a coaxal system by a constant. The Tucker circles are a coaxaloid system (Johnson 1929, p. 277).

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

A cross section of a solid is a plane figure obtained by the intersection of that solid with a plane. The cross section of an object therefore represents an infinitesimal ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

Draw a triangle DeltaA_1A_2A_3, and let A_1^' be the intersection of the parallel to A_3A_1 through A_2 (the A_2-exmedian) and the parallel to A_1A_2 through A_3 (the ...