Hi Michel,

I would like to know if there is a method I can use
in the geo file to split the square by the other diagonal

Look at Transfinite Surface command with <Left | Right | Alternate> arguments for the way the triangles will oriented.

and a method to split the square in 4 triangles
still with the diagonals

I don't know about that, but maybe Transfinite Surface with Alternate argument can be a kind of what you want.

Regards,
Mikhail

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