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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