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A quadric is said to be non-degenerate if the matrix is invertible. A non-degenerate quadric is non-singular in the sense that its projective completion has no singular point (a cylinder is non-singular in the affine space, but it is a degenerate quadric that has a singular point at infinity).
The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
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Labs surface, a certain septic with 99 nodes; Endrass surface, a certain surface of degree 8 with 168 nodes; Sarti surface, a certain surface of degree 12 with 600 nodes; Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue ...
A Scherk surface. Catalan's minimal surface; Costa's minimal surface; Catenoid; Enneper surface; Gyroid; Helicoid; Lidinoid; Riemann's minimal surface; Saddle tower; Scherk surface; Schwarz minimal surface; Triply periodic minimal surface
The generators of any ruled surface coalesce with one family of its asymptotic lines. For developable surfaces they also form one family of its lines of curvature. It can be shown that any developable surface is a cone, a cylinder, or a surface formed by all tangents of a space curve. [5] Developable connection of two ellipses and its development
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