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A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

A plesiohedron is the Voronoi cell of a so-called symmetric Delone set. Plesiohedra are space-filling polyhedra which have special symmetries that take any copy of the ...

In elliptic n-space, the flat pole of an (n-1)-flat is a point located an arc length of pi/2 radians distant from each point of the (n-1)-flat. For an n-dimensional spherical ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. For M in R^3, the second fundamental form is the symmetric bilinear form on the tangent ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

A skew conic, also known as a gauche conic, space conic, twisted conic, or cubical conic section, is a third-order space curve having up to three points in common with a ...