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A regular patch is a patch x:U->R^n for which the Jacobian J(x)(u,v) has rank 2 for all (u,v) in U. A patch is said to be regular at a point (u_0,v_0) in U provided that its ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

A spherical shell is a generalization of an annulus to three dimensions. A spherical shell is therefore the region between two concentric spheres of differing radii. The ...

A ball of radius 1.

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

The genesa is a mystical figure that correspond to a spherical cuboctahedron.