Great Respect to Gordo, but
Screen Dainippon offer really a great number of types of dot shapes, but the angles are constraint to C 15, M 45, Y 90/0, K 75. This is by default. In most practical cases these angles are Ok. There is some strange Japanese logic for this setting.
TF1-724SQU01H-12 means Trueflow1, 2400 dpi Square dot, High lpi, 12 bit coding, but the 7 means that all screen angles are +7.5deg for flexo. This can be the reason for strange looking.
Best Regards,
Ansoft
I just think that Screen should provide info regarding their dot shapes (Harlequin and Heidelberg do a pretty good job of this).
The 7.5 degree angle offset is not just for flexo. It's a way to add noise to the halftone screen in order to avoid single channel moiré.
Do you have an image of what the "Square" dot looks like that you could post?
I almost think it was screens answer to high LPI screen sets like fuji's co-res, because it starts at 210, but goes up to like 360, I have tried 230, but never had the stones to go higher, worried I would get smaller dots at the price of less image depth...