The title prompt produces the following outputs when I try it on some prominent models (along with an image of an icosahedron in the real world):
None of these are even close to an acceptable image by my standards, though in other trials Stable Diffusion has fared somewhat better.
On 2023-06-01, I will go through every SoTA image model I am aware of and have access to, and obtain four generations from the prompt "A regular icosahedron carved out of wood". I'll settle to YES if any of the models tested yield a success on at least two of the four samples, where a success requires:
All or almost all of the polyhedron is in frame
It is clearly made out of wood
It has well-defined faces that clearly meet along edges and vertices
The faces are pretty close to equilateral (small deviation is OK)
Exactly five faces meet at every vertex
The perspective shown is physically realizable with some orientation of an icosahedron
For comparison, using this prompt with "cube" instead of "icosahedron" gives outputs that easily pass all the above requirements on SD2 and DALL-E, and kind of marginal outputs on MidJourney.
Fine-tuned models won't count, only general-purpose image models that haven't specifically focused on icosahedra or geometric objects or something.
I'll resolve early if there's a model before the resolution date that completely crushes this prompt, but I won't if it only sometimes gets it right (since it might still be the case that I get unlucky draws when sampling on 2023-06-01). I'll accept samples from non-public models if a commenter can credibly exhibit them.
I won't bet in this market.
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@jacksonpolack it's Midjourney v5.1 but I admit I cheated with the prompt and asked for "a d20 carved out of wood"
It seems MJ has no problem making regular icosahedrons, but the wood grain is confusing it. I think it's because it has 'horror vacui' and the grain of the wood acts as a seed for extra complexity.
Still, by lowering the 'style' setting it makes stuff that's alost acceptable, for example this one is almost ok if not for the fact there's six faces on the lower side.
The prompt was: "a regular icosahedron carved out of wood with flat faces"
@jacksonpolack It only fails at one of the six listed criteria, I don't think it's that far off, admittedly the deadline is pretty close.
@NathanHelmBurger update: tried again with stable diffusion 2023-05-17. Still not good.
Betting YES because I think icosahedra are common enough that a future model will include some in its training data and learn by rote what they look like. I doubt we'll have an image model that can create arbitrary geometric shapes by then.
(I had some fun playing around with DALL-E and geometry/topology a while back, and it was absolutely terrible at stuff like this.)
@IsaacKing Interesting that "d20" seems to work a little better than "icosahedron"! (Though still not well enough that its performance would currently qualify.)
