Bour's Minimal Surface
Gray (1997) defines Bour's minimal curve over complex 
by
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(1)
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(2)
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(3)
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and then derives a family of minimal surfaces.
The order-three Bour surface resembles a cross-cap and is given using Enneper-Weierstrass parameterization by
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(4)
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(5)
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or explicitly by the parametric equations
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(6)
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(7)
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(8)
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(Maeder 1997). It is an algebraic surface of order 16.
The coefficients of the first fundamental form are given by
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(9)
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(10)
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(11)
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and the coefficients of the second fundamental form by
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(12)
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(13)
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(14)
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The area element is
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(15)
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The Gaussian and mean curvatures are given by
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(16)
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(17)
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bour's minimal surface
