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The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...

A rose curve, also called Grandi's rose or the multifolium, is a curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician ...

A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

Togliatti surfaces are quintic surfaces having the maximum possible number of ordinary double points (31). A related surface sometimes known as the dervish can be defined by ...

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = ...

Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

A heptahedron is a polyhedron with seven faces. Because there are 34 heptahedral graphs, there are 34 topologically distinct convex heptahedra. There are three semiregular ...