ISTANBUL - Every three cushion player must have noticed this at some point: not all billiards have rails of the same width. But we only play on the green cloth, which is invariably 1.42,25 x 2.84,50 cm. So is there a consequence? Yes there is. American billiard scientist Ira Lee had noted this earlier, and now Murat Tüzül joins him. He is the author of a well-respected book about diamond systems. If you aim at the heart of a diamond in the rail (at an angle), you will hit the cloth of the rubber much earlier.
The application of diamond systems is therefore (co)dependant on the placement of the diamond signs in the wood of the rail. Let's hear from the Turkish author and 3-cushion player himself:
Dear three cushion billiard friends,
I would like to make to point out a subject which, I think is neglected so far. I want to thank the "Kozoom Team" for giving me the opportunity to share my opinions with you.
No one feels the necessity for deliberating upon UMB and CEB's recognised modern billiards standards for table dimensions, diamond distances, ball measurements and weight, which are a consequence of an evolution on the materials of billiards; and this is natural and utterly true.
Nevertheless, I consider that, the distance from the center of a diamond to the edge of the cushion should be standardized, at least on the basis of meterage on every table, in order to ensure invariable implementation of billiard systems, one of the indispensable elements of modern billiards.
When my curiosity on the matter increased, I wondered how this matter has been ignored and not brought forward so far. Furthermore, as I've set my heart on billiards for 25 years and have been engaged to the mathematical aspect, I am still angry with myself for not having any questions on this subject. However, I am slightly happy to be one of the first to perceive the matter.
When I measured up different tables, I examined that the distance from the center of a diamond to the edge of the cushion were not identical, on the tables of different labels. Consequently, I may easily state that all the table manufacturers place the diamonds in different metric measures.
My hypothesis is a result of my theoretical studies and may be confirmed by the samples about the "Diamond System" in master Raymond Ceulemans' work "Mister 100", which is accepted by the whole billiards world as a strong mathematical reference. Once again, this is a hypothesis. The verification of this hypothesis is possible with a serious scientific work of mathematicians. I see no harm in sharing my work on the matter, wishing you to review taking all these into account. Not just for expressing opinions but putting forward proposals standing on a strong base line will help our sport to improve and at least to standardize the materials.
My work has been sent to UMB as a suggestion letter, I believe that the matter will be handled delicately.
Best regards...
Murat Tüzül
About the graphic B:
The drawings are scaled an vectorial.
A billiards table is made up of two identical squares.
In this hypothesis the streching of the cushion or which direction the ball goes has no importance.
The calculation is based on the assumption that, accepting the distance between two diamonds as X units, when you hit a ball on the short cushion from the lower left-hand corner to right hand-side from 3X distance, and on the long cushion from the lower right-hand corner to the upper side from 6X distance, it should arrive the 0 point.
This proportion of 1 to 2 is not occasional. The hypothesis is based on this proportion. Under these circumstances the distance between the edge of the cushion and the center of the diamond should be 7,7672 cm, rounding up 7,8 cm.
In my estimation, it allows to use the systems in ±0,5 cm tolerance.
Click both Graphics to enlarge.
A: 
B: 