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Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

A parametric latitude which gives a sphere equal surface area relative to an ellipsoid. The authalic latitude is defined by beta=sin^(-1)(q/(q_p)), (1) where ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

A rhombohedron is a parallelepiped bounded by six rhombi such that opposite faces are congruent. A rhombohedron having all six rhombic faces congruent is known as a trigonal ...

A compact manifold is a manifold that is compact as a topological space. Examples are the circle (the only one-dimensional compact manifold) and the n-dimensional sphere and ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

Fisheye perspective is a two-part projection. First, three-dimensional space is projected onto the surface of a hemisphere, by connecting every external point to the center ...

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...