A minimal surface discovered by L. P. M. Jorge and W. Meeks III in 1983 with Enneper-Weierstrass parameterization
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(1)
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(2)
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(Dickson 1990). Explicitly, it is given by
 |  | ![R[(re^(itheta))/(3(1+re^(itheta)+r^2e^(2itheta)))-(4ln(re^(itheta)-1))/9+(2ln(1+re^(itheta)+r^2e^(2itheta)))/9]](/images/equations/Trinoid/Inline9.svg) |
(3)
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 |  | ![-1/9I[(-3re^(itheta)(1+re^(itheta)))/(r^3e^(3itheta)-1)+(4sqrt(3)(r^3e^(3itheta)-1)tan^(-1)((1+2re^(itheta))/(sqrt(3))))/(r^3e^(3itheta)-1)]](/images/equations/Trinoid/Inline12.svg) |
(4)
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 |  | ![R[-2/3-2/(3(r^3e^(3itheta)-1))].](/images/equations/Trinoid/Inline15.svg) |
(5)
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The coefficients of the first fundamental form are given by
 |  | ![((1+r^4)^2)/([1+r^6-2r^3cos(3phi)]^2)](/images/equations/Trinoid/Inline18.svg) |
(6)
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(7)
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 |  | ![(r^2(1+r^4)^2)/([1+r^6-2r^3cos(3phi)]^2),](/images/equations/Trinoid/Inline24.svg) |
(8)
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and the coefficients of the second fundamental form by
 |  | ![(8r^4-4r(1+r^6)cos(3phi))/([1+r^6-2r^3cos(3phi)]^2)](/images/equations/Trinoid/Inline27.svg) |
(9)
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 |  | ![(4r^2(r^6-1)sin(3phi))/([1+r^6-2r^3cos(3phi)]^2)](/images/equations/Trinoid/Inline30.svg) |
(10)
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 |  | ![(4r^3(1+r^6)cos(3phi)-8r^6)/([1+r^6-2r^3cos(3phi)]^2).](/images/equations/Trinoid/Inline33.svg) |
(11)
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The area element is
![dA=(r(1+r^4)^2)/([1+r^6-2r^3cos(3phi)]^2)dr ^ dphi.](/images/equations/Trinoid/NumberedEquation1.svg) |
(12)
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The Gaussian and mean curvatures are given by
 |  | ![-(16r^2[1+r^6-2r^3cos(3phi)]^2)/((1+r^4)^4)](/images/equations/Trinoid/Inline36.svg) |
(13)
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(14)
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