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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. ...

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

A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical ...

The edge of a polygon or face of a polyhedron are sometimes called sides.

The analog of trilinear coordinates for tetrahedra.

A space endowed with a non-Euclidean elliptic geometry.

In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then 1/(AB)+1/(CD)=1/(EF). A beautiful related theorem due to H. Stengel can be stated ...

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

An affine transformation in which the scale is reduced.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.