If you have a straight line of cubes together you only need a gap of 1 – 2mm between each one to maintain one, continuous line. Put this line of cubes on a curve though and a gap will open up between each one on the outside edge. This gap is in the shape of a triangle.

 

To maintain continuity in your mosaic it does obviously need to be filled in with something. If you use triangular shaped tesserae then this causes a disruption to the ‘flow’ of the line. The 2nd line illustrated to the left here shows another incorrect way to attempt to fill the gaps by using thinner tesserae resulting in a fan pattern, but this tends to be an error I see in modern reproduction work now.

 

The Roman mosaicists kept the 'flow' of the line by opening the gaps a little further and then used the cut keystone shaped tesserae to maintain the flow of the line. They only needed to do this on certain areas of the curve as the tesserae they used were all slightly irregular anyway. You'll find that you can open up the gaps by slight adjustment and taking advantage of the irregular edges. You will have to look carefully to see examples of the keystone cuts in use but they are there.

 

 

 

 

 

 

 

 

 

 

The exception to this rule is when you have an angle which is too sharp, ie like the inside black lines on the Guilloche pattern in the image below.