D3 forms for the Minkowksi ansatz
As mentioned below, the Minkowksi ansatz gives rise to 23 D3 forms. The connection matrices and various other useful data about these D3 forms are here. This list contains 15 of the 17 minimal Fano varieties and several other currently-mysterious examples. Some of these look like they could be G-Fanos. The original data, without annotations, are here: MinkowskiD3Matrices.
Sergei: please can you take a look at this list and see whether you can fill in the gaps.