Shield of concentric curved triangles.
Later today I'll post up how to set this out for your size of tesserae. The pattern is known as Phyllotaxis but for a mosaic you have to add more concentric rings to create the triangles. The smallest I've worked this out (using average 11mm - 7/16" tesserae) is a diameter of 305mm - 12".
The curved lines may look a little rough, you'll see why when you draw this out yourself, but it's not a problem as you tidy them up when you set the tesserae.