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BISPHERICAL ALGEBRAIC SURFACE

An algebraic surface is said to be *bispherical* if the umbilics (i.e. the points at infinity of the complex sphere with zero radius ) form a double line, in the complex projective completion of the space.

The necessary and sufficient condition is that the polynomial composed of the terms with highest degree *n* of its Cartesian equation be divisible by and that the polynomial composed of the terms of with degree *n* - 1 be divisible by .

The bispherical quartics are the Darboux cyclides.

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© Robert FERRÉOL 2017