Can I draw platonic solid inside a Bloch sphere?

I wonder if there's a tool available to draw platonic solids or other 3-D shapes inside a Bloch sphere. Here's an example I found on a research paper: In my previous visualizations, I used the kaleidoscope package in Python to simulate time-evolution inside the Bloch sphere. I wonder if there's a tool I could draw 3-D shapes also. Thanks!

• I mean, the "Bloch sphere" is just a sphere, so aren't you just asking "can I draw platonic solids inside a sphere?"? Or do you mean some sort of expression for the quantum states corresponding to the vertices of a platonic solid inscribed in a sphere?
– glS
Aug 4 '21 at 23:27
• @glS Thanks for the comment! I'll be generating quantum states corresponding to the vertices of 3D shapes. I could visualize the states as scatters or vectors on the Bloch sphere, but I don't know how can I connect those vertices (or which tools I could use), like the example diagram:)
– ZR-
Aug 4 '21 at 23:31
• so you justmean how to draw those graphics really, regardless of the underlying interpretation as quantum states? Tbh I'm not sure that this is particularly OT in this site, but anyway, you can do this sort of thing pretty easily with Mathematica. E.g. Graphics3D[{Opacity@0.4, Sphere[], Dodecahedron[0.72]}] generates i.stack.imgur.com/Ejoku.png. Figuring out the expression for the vertices you can also easily highlight them. You can also have a look at mathematica.stackexchange.com/q/125985/27539 for how to draw a fancier Bloch sphere with MMA
– glS
Aug 4 '21 at 23:36
• @Martin Vesely Yeah of course! researchgate.net/publication/…
– ZR-
Aug 5 '21 at 16:12
• These are also relevant for rotation sensing with Majorana constellations; eg arxiv.org/abs/1612.06804, arxiv.org/abs/1002.2158, etc Aug 6 '21 at 2:56