Classic

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Roman Surface

An immersion of the projective plane with 4 cross caps
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Boy's Surface

An immersion of the projective plane with 1 triple point
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Cayley's Cubic

x^2+y^2+z^2
+4 x y z=1/4
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Dupin's Cyclide

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Hunt's Surface

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Bohemian Dome

Envelope of a circle rotated about a circle. Thanks to John Ckertok for this.
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Bohemian Star

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Diagonal surface of Clebsch

A cubic with 27 straight lines
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Cassini's Surface
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Miter Surface