Three views of the (real part of the) Klein quartic $x^3y+y^3z+z^3x=0$ with Mathematica - well, two copies of it on the 2-sphere as explained in the comment by Heinrich Hartmann, that is, individual points in the projective plane are represented by pairs of diametrally opposite points on the sphere.

Of course in Mathematica you can turn it around to view from different sides.

Code:

```
Show[
{
Graphics3D[{Opacity[.1], Sphere[]}],
RegionPlot3D[
Abs[x^3 y + y^3 z + z^3 x] < .02 \[And] Abs[x^2 + y^2 + z^2 - 1] < .03,
{x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1},
PlotPoints -> 100, Mesh -> None
]
}
,Boxed -> False]
```