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A surface of constant Gaussian curvature that can be given parametrically by x = a(Ucosu-U^'sinu) (1) y = -a(Usinu+U^'cosu) (2) z = v-aV^', (3) where U = ...

An orientable surface with one boundary component such that the boundary component of the surface is a given knot K. In 1934, Seifert proved that such a surface can be ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

An algebraic surface of degree 12. Examples of dodecic surfaces include the figure-eight parametrization of the Klein bottle and Sarti dodecic.

A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

A quartic surface named after its resemblance to the liturgical headdress worn by bishops and given by the equation 4x^2(x^2+y^2+z^2)-y^2(1-y^2-z^2)=0.

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...