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Boy Surface

Example plot

Example plot

Equations

x(u, v) = (a (sqrt(2) cos(2 u) cos^2(v) + cos(u) sin(2 v)))/(2 - sqrt(2) sin(3 u) sin(2 v)) y(u, v) = (a (sqrt(2) sin(2 u) cos^2(v) + cos(u) sin(2 v)))/(2 - sqrt(2) sin(3 u) sin(2 v)) z(u, v) = (3 a cos^2(v))/(2 - sqrt(2) sin(3 u) sin(2 v))

81 a^2 x^2 z^2 - 162 a^2 x y z^2 + 54 sqrt(2) a^2 x z^3 + 81 a^2 y^2 z^2 - 54 sqrt(2) a^2 y z^3 + 18 a^2 z^4 - 486 a x^3 y z + 1458 a x^2 y^2 z - 324 sqrt(2) a x^2 y z^2 - 216 a x^2 z^3 - 1458 a x y^3 z + 486 sqrt(2) a x y^2 z^2 + 216 a x y z^3 - 144 sqrt(2) a x z^4 + 486 a y^4 z - 162 sqrt(2) a y^3 z^2 - 216 a y^2 z^3 + 108 sqrt(2) a y z^4 - 48 a z^5 + 729 x^6 - 2916 x^5 y + 486 sqrt(2) x^5 z + 5103 x^4 y^2 - 972 sqrt(2) x^4 y z - 162 x^4 z^2 - 5832 x^3 y^3 + 972 sqrt(2) x^3 y^2 z + 1296 x^3 y z^2 - 216 sqrt(2) x^3 z^3 + 5103 x^2 y^4 - 972 sqrt(2) x^2 y^3 z - 2106 x^2 y^2 z^2 + 432 sqrt(2) x^2 y z^3 + 72 x^2 z^4 - 2916 x y^5 + 486 sqrt(2) x y^4 z + 1944 x y^3 z^2 - 540 sqrt(2) x y^2 z^3 - 144 x y z^4 + 96 sqrt(2) x z^5 + 729 y^6 - 648 y^4 z^2 + 108 sqrt(2) y^3 z^3 + 108 y^2 z^4 - 48 sqrt(2) y z^5 + 32 z^6 = 0

Surface properties

6

Metric properties

g_(uu) = (a^2 ((3 sqrt(2) cos(3 u) sin(2 v) (sqrt(2) sin(2 u) cos^2(v) + cos(u) sin(2 v)) + (2 - sqrt(2) sin(3 u) sin(2 v)) (2 sqrt(2) cos(2 u) cos^2(v) - sin(u) sin(2 v)))^2 + (3 sqrt(2) cos(3 u) sin(2 v) (sqrt(2) cos(2 u) cos^2(v) + cos(u) sin(2 v)) + (sqrt(2) sin(3 u) sin(2 v) - 2) (sin(u) sin(2 v) + 2 sqrt(2) sin(2 u) cos^2(v)))^2 + 648 cos^2(3 u) sin^2(v) cos^6(v)))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(uv) = (2 a^2 (27 sqrt(2) cos(3 u) sin(v) cos^4(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v)) + 2 (6 (cos(u) + cos(5 u)) sin(v) cos^3(v) - 4 sin(2 u) cos^2(v) (sqrt(2) - sin(3 u) sin(2 v)) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v))) + 2 (4 sqrt(2) cos(2 u) cos^2(v) - 4 (sin(u) + sin(5 u)) sin(v) cos^3(v) + 6 sin(2 u) cos(3 u) sin(2 v) cos^2(v) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(vu) = (2 a^2 (27 sqrt(2) cos(3 u) sin(v) cos^4(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v)) + 2 (6 (cos(u) + cos(5 u)) sin(v) cos^3(v) - 4 sin(2 u) cos^2(v) (sqrt(2) - sin(3 u) sin(2 v)) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v))) + 2 (4 sqrt(2) cos(2 u) cos^2(v) - 4 (sin(u) + sin(5 u)) sin(v) cos^3(v) + 6 sin(2 u) cos(3 u) sin(2 v) cos^2(v) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(vv) = (a^2 (9 cos^2(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v))^2 + 4 (2 cos(u) cos(2 v) + cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))^2 + 4 (2 cos(u) cos(2 v) + sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))^2))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4

Vector properties

left double bracketing bar x(u, v) right double bracketing bar = (a sqrt(2 sqrt(2) sin(v) cos^3(v) (sin(u) + sin(3 u) + cos(u) + cos(3 u)) + 2 cos^2(u) sin^2(2 v) + 11 cos^4(v)))/(2 - sqrt(2) sin(3 u) sin(2 v))

N^^(u, v) = -(3 cos^2(v) (60 sin(u) + 32 sin(5 u) + 4 sin(7 u) - 6 sin(u - 4 v) + sqrt(2) sin(4 u - 4 v) - 8 sin(5 u - 4 v) - 2 sin(7 u - 4 v) - sqrt(2) sin(8 u - 4 v) - 8 sin(u - 2 v) + 40 sqrt(2) sin(2 u - 2 v) + 2 sqrt(2) sin(4 u - 2 v) + 8 sin(5 u - 2 v) - 2 sqrt(2) sin(8 u - 2 v) - 40 sqrt(2) sin(2 (u + v)) - sqrt(2) sin(4 (u + v)) - 8 sin(u + 2 v) - 2 sqrt(2) sin(4 u + 2 v) + 8 sin(5 u + 2 v) + 2 sqrt(2) sin(8 u + 2 v) - 6 sin(u + 4 v) - 8 sin(5 u + 4 v) - 2 sin(7 u + 4 v) + sqrt(2) sin(8 u + 4 v)))/(abs(cos(v)) sqrt(576 (4 cos(2 v) sin(2 u) sin(3 u) (sqrt(2) sin(3 u) sin(2 v) - 2) cos^3(v) + 4 sqrt(2) sin(2 u) sin(v) (sin^2(3 u) sin^2(2 v) + 2) cos^2(v) + (-16 (2 cos(u) + cos(3 u)) sin^2(u) sin^2(2 v) + 6 cos(u) cos(3 u) cos(2 v) (sin(3 u) sin(2 v) - sqrt(2)) sin(2 v) + sin(u) (8 sin^2(v) + sin(3 u) (sin(3 u) sin(2 v) - sqrt(2)) sin(4 v))) cos(v) + sin(v) sin^2(2 v) (2 sin(u) sin(3 u) (sin(3 u) sin(2 v) - 2 sqrt(2)) + cos(u) (3 sin(6 u) sin(2 v) - 6 sqrt(2) cos(3 u))))^2 + 9 cos^2(v) (-60 sin(u) - 32 sin(5 u) - 4 sin(7 u) + 6 sin(u - 4 v) - sqrt(2) sin(4 u - 4 v) + 8 sin(5 u - 4 v) + 2 sin(7 u - 4 v) + sqrt(2) sin(8 u - 4 v) + 8 sin(u - 2 v) - 40 sqrt(2) sin(2 u - 2 v) - 2 sqrt(2) sin(4 u - 2 v) - 8 sin(5 u - 2 v) + 2 sqrt(2) sin(8 u - 2 v) + 40 sqrt(2) sin(2 (u + v)) + sqrt(2) sin(4 (u + v)) + 8 sin(u + 2 v) + 2 sqrt(2) sin(4 u + 2 v) - 8 sin(5 u + 2 v) - 2 sqrt(2) sin(8 u + 2 v) + 6 sin(u + 4 v) + 8 sin(5 u + 4 v) + 2 sin(7 u + 4 v) - sqrt(2) sin(8 u + 4 v))^2 + cos^2(v) (-18 sqrt(2) cos(u) + 14 sqrt(2) cos(3 u) - 2 sqrt(2) cos(5 u) + 4 sqrt(2) cos(7 u) + 2 sqrt(2) cos(9 u) + sqrt(2) cos(u - 4 v) - 6 cos(2 u - 4 v) + sqrt(2) cos(3 u - 4 v) - 6 cos(4 u - 4 v) + sqrt(2) cos(5 u - 4 v) - 2 cos(6 u - 4 v) - 2 sqrt(2) cos(7 u - 4 v) - sqrt(2) cos(9 u - 4 v) + 24 sqrt(2) cos(u - 2 v) - 4 cos(2 u - 2 v) + 8 sqrt(2) cos(3 u - 2 v) + 20 cos(4 u - 2 v) + 4 cos(6 u - 2 v) + 4 cos(2 (u + v)) + 6 cos(4 (u + v)) + 24 sqrt(2) cos(u + 2 v) + 8 sqrt(2) cos(3 u + 2 v) - 20 cos(4 u + 2 v) - 4 cos(6 u + 2 v) + sqrt(2) cos(u + 4 v) + 6 cos(2 u + 4 v) + sqrt(2) cos(3 u + 4 v) + sqrt(2) cos(5 u + 4 v) + 2 cos(6 u + 4 v) - 2 sqrt(2) cos(7 u + 4 v) - sqrt(2) cos(9 u + 4 v) - 18 sqrt(2) sin(u) + 70 sqrt(2) sin(3 u) + 2 sqrt(2) sin(5 u) + 4 sqrt(2) sin(7 u) + 2 sqrt(2) sin(9 u) + sqrt(2) sin(u - 4 v) + 6 sin(2 u - 4 v) - 11 sqrt(2) sin(3 u - 4 v) - 6 sin(4 u - 4 v) - sqrt(2) sin(5 u - 4 v) - 6 sin(6 u - 4 v) - 2 sqrt(2) sin(7 u - 4 v) - sqrt(2) sin(9 u - 4 v) + 24 sqrt(2) sin(u - 2 v) + 4 sin(2 u - 2 v) + 24 sqrt(2) sin(3 u - 2 v) + 20 sin(4 u - 2 v) - 4 sin(6 u - 2 v) - 120 sin(2 v) - 12 sin(4 v) - 4 sin(2 (u + v)) + 6 sin(4 (u + v)) + 24 sqrt(2) sin(u + 2 v) + 24 sqrt(2) sin(3 u + 2 v) - 20 sin(4 u + 2 v) + 4 sin(6 u + 2 v) + sqrt(2) sin(u + 4 v) - 6 sin(2 u + 4 v) - 11 sqrt(2) sin(3 u + 4 v) - sqrt(2) sin(5 u + 4 v) + 6 sin(6 u + 4 v) - 2 sqrt(2) sin(7 u + 4 v) - sqrt(2) sin(9 u + 4 v))^2))

Properties

algebraic surfaces | nonorientable surfaces | sextic surfaces

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Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

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Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

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Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.

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