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A sphere with a single cross-cap. This term is more appropriate in purely topological applications than the more common term real projective plane, which implies the presence ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

The surface with three cross-caps (Francis and Collins 1993, Francis and Weeks 1999).

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = au^4+u^2v-v^2. (3)

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

An oriented surface for which every point belongs to a Wiedersehen pair. Proof of the Blaschke conjecture established that the only Wiedersehen surfaces are the standard ...

The Kummer surfaces are a family of quartic surfaces given by the algebraic equation (x^2+y^2+z^2-mu^2w^2)^2-lambdapqrs=0, (1) where lambda=(3mu^2-1)/(3-mu^2), (2) p, q, r, ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

In affine three-space the Cayley surface is given by x_3=x_1x_2-1/3x_1^3 (1) (Nomizu and Sasaki 1994). The surface has been generalized by Eastwood and Ezhov (2000) to ...