Qutrit quantum states

Set of states of a qutrit is 8-dimensional and has intricate geometry, which we can observe by studying its projections to lower dimensions. In the article
https://arxiv.org/abs/1603.06569 the possible geometries of three-dimensional projections were studied, and representatives of possible classes are presented here. The objects are always convex, so they are only differentiated by their bondary features.
For a random projection space, the resulting object (a three-dimensional projection of the 8-dimensional set of states) is a smooth oval. However, it is possible to fine-tune the projection space and obtain objects with various flat parts, which are images of qubit spaces embedded within a qutrit. Classification in the terms of these flat parts goes as follows:

• One ellipse, zero segments (e1s0.stl, see Example 6.2 of the article for the defining matrices),
• Two ellipses, zero segments (e2s0.stl, Example 6.3),
• Three ellipses, zero segments (e3s0.stl, Example 6.4),
• Four ellipses, zero segments (e4s0.stl, Example 6.5 – convex hull of Steiner surface),
• Zero ellipses, one segment (e0s1.stl, Example 6.6),
• One ellipse, one segment (e1s1.stl, Example 6.7),
• Two ellipses, one segment (e2s1.stl, Example 6.8).

Apart from this are degenerated examples, for which the defining matrices split into qubit and one-dimensional part: they correspond to convex hulls of qubit state space (a Bloch ball, possibly flattened to an ellipse, segment, or a point) and an arbitrary point.

The 3D objects print without any issues without supports if placed on one of the faces, although the lower parts with overhang surfaces may look rough. For best looking results it might be advisable to split a part across a symmetry plane and then glue it back into a single object. The objects are not scaled to print, and the raw STL coordinates are the projection points; if these are interpreted as milimiters (usual), the models are tiny, so please scale up to a desired size.

For the Mathematica notebook with the calculations of the objects see https://github.com/knszm/3d-jnr, and https://quantumstat.es/note/Two-qubit-3D-JNR for a work in progress related to the analogous question with two qubits instead of a qutrit.