Enneper surface and its base

thingiverse

Enneper surface Enneper surface is a self-intersecting surface which was introduced by Alfred Enneper 1864 in connection with minimal surface theory. The equation for enneper's surface is 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0 which can also be described parametrically: x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3 Enneperi pind Enneperi pinnaks nimetatakse ennastlõikavat pinda, mis loodi Alfred Enneperi poolt aastal 1864 minimaalse pinnateooria ühe osana. Enneperi pinna valemiks on 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0, mida saab anda edasi ka parameetriliste võrrandite abil: x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 ja z = (u²-v²)/3