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Eistute -- singular algebraic surface
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Eistute, a singular algebraic surface of degree six. This is the set of real points for which
```
(x^2+y^2)^3-4*x^2*y^2*(z^2+1) = 0.
```
Has a singular line -- the z-axis! When you compute points on it, you get them 16 times!
I have provided these files:
* `Eistute_thickened_Smooth_repaired.stl` -- has the normal vectors fixed, and is thickened for printing.
* `eistute_raw_correct.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for 4- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. The raw versions are not directly suitable for 3d printing.
* `eistute_raw_smooth.stl` -- infinitely thin, ran through `sampler` with fairly tight tolerances.
* `input` -- the Bertini_real inpu
```
(x^2+y^2)^3-4*x^2*y^2*(z^2+1) = 0.
```
Has a singular line -- the z-axis! When you compute points on it, you get them 16 times!
I have provided these files:
* `Eistute_thickened_Smooth_repaired.stl` -- has the normal vectors fixed, and is thickened for printing.
* `eistute_raw_correct.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for 4- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. The raw versions are not directly suitable for 3d printing.
* `eistute_raw_smooth.stl` -- infinitely thin, ran through `sampler` with fairly tight tolerances.
* `input` -- the Bertini_real inpu
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