Algebraic Surface -- from Wolfram MathWorld

The set of roots of a polynomial . An algebraic surface is said to be of degree , where is the maximum sum of powers of all terms . The following table lists the names of algebraic surfaces of a given degree.

order	surface	examples
2	quadratic surface	cone, cylinder, ellipsoid, elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder, hyperbolic paraboloid, paraboloid, sphere, spheroid
3	cubic surface	Cayley cubic, Clebsch diagonal cubic, ding-dong surface, handkerchief surface, Möbius strip, monkey saddle, shoe surface, Wallis's conical edge, Whitney umbrella
4	quartic surface	apple surface, Bohemian dome, Cassini surface, Cayley cubic Hessian, cross-cap, crossed trough, cushion surface, double sphere, eight surface, elliptic torus, Goursat's surface, Klein quartic surface, lemon surface, Menn's surface, miter surface, Nordstrand's weird surface, Peano surface, piriform surface, quartoid, Roman surface, Steiner surface types 2 and 4, tanglecube, tooth surface, torus
5	quintic surface	dervish, kiss surface, swallowtail catastrophe surface, Togliatti surface
6	sextic surface	Barth sextic, Boy surface, heart surface, Hunt's surface, sine surface
7	septic surface	Labs septic
8	octic surface	Endraß octic, oloid
9	nonic surface	Enneper's minimal surface
10	decic surface	Barth decic
12	dodecic surface	Klein bottle, Sarti dodecic
15	pentadecic surface	Henneberg's minimal surface
16	hexadecic surface	Bour's minimal surface

References

Banchoff, T. F. "Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order." In Geometric Analysis and Computer Graphics: Proceedings of a Workshop Held May 23-25, 1988 (Eds. P. Concus, R. Finn, D. A. Hoffman). New York: Springer-Verlag, pp. 31-37, 1991.

Beutel, E. Algebraische Kurven. Leipzig, Germany: Teubner, 1909.

Algebraic Surface

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