Can a Johnson solid be optimised into a nearly fair d26? Looking for simulation help

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I'm investigating whether the \*\*elongated square gyrobicupola (Johnson solid J37)\*\* can be modified into a reasonably fair 26-sided die.

I've already spent quite a while looking at the numbering problem. The 26 faces fall into symmetry classes, and I've produced a numbering that equalises the average value of each class and balances the numbers as well as I can. I think the numbering is now "good enough" that the remaining bias will be dominated by the geometry rather than the numbering.

The question I'm interested in is purely geometric.

Imagine starting with a cube of side length \*\*1\*\* and constructing the shape by making a sequence of cuts.

The parameters would be something like:

\* depth of the edge cuts,

\* depth of the vertex cuts,

\* angle of the vertex cuts,

\* and possibly (if necessary) allowing the upper and lower vertex cuts to use different angles, giving a total of up to \*\*five variables\*\*.

The goal is to find whether there is a region in this parameter space that minimises bias and produces the fairest possible d26.

I'm \*\*not\*\* expecting a perfectly fair die—I'd just like to know whether an optimum exists, and roughly what those dimensions would be.

Ideally I'd like have a helpful person run a large number of rigid-body simulations (Blender, Bullet, MuJoCo, PhysX, Unity, custom code—whatever is appropriate), varying the parameters across the search space and recording the landing frequencies for each face.

Questions:

\* Has anyone attempted something similar?

\* If you have experience with rigid-body simulation or procedural geometry, would you be interested in helping investigate it?