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Explaining the common diamond parameters
The first C: Carat
The first C, Carat, is a measure for the weight of a diamond. This unit is also used to describe the weight of other gemstones. Historically the word "carat" came from the Greek word "keration" translated as "fruit of the carob tree". The seeds of the carob tree where used in the middle east, in ancient times, as a reference for weighing gold and gemstones. Later on the carat (ct) was defined as 0.2 gram. Each carat is divisible in hundreds of a carat, named points.
So, as an example, a 1.35 ct diamond (one carat and thirty five points) weighs 0.27 g.
The weight of a diamond has an important impact on the price.
The second C: Color
First we make the distinction between "white" diamonds and colored diamonds. The diamonds used for jewels are mostly "white" diamonds. White diamonds are bright white to fainted yellow. The amount of yellow, caused by nitrogen, determines the prize. The more yellow the lower the price. A color scale is used to categorize the diamond color. The color scale ranges from D (colorless) to M (fainted yellow). Depending on the grading lab the colors behind M are determined as fancy yellow.
An aspect influencing the color is fluorescence. This represents the ability of a diamond to transform UV light to visible light. The amount of fluorescence is described as nil, faint, medium, strong and very strong. The exact syntax depends on the grading labs. Depending on the amount and the color of fluorescence, the diamond will look whiter. This appears when the conversion of the UV light results in displaying blue light, a complementary color of yellow. In some cases the amount of fluorescence is so high that the diamond looks "milky white". This effect only appears with very strong fluorescence. The degree of fluorescence influences the price discount to compensate for an overestimation of the color. 
The third C: Clarity
The clarity gives an indication of the internal defects present in a diamond. The clarity grade is assessed using a 10x loupe. In grading labs the graders use a stereo microscope with a bigger magnification but even then the final decision is checked against the loupe 10x.
The clarity depends on:
The size
The bigger the size of the clarity characteristic, the lower the clarity grade.
The number
The more, clearly visible, internal characteristics, the lower the clarity grade.
The position

If an inclusion is located near the table or near the culet the grade is lowered more than if it is located nearby the girdle. If the position of the inclusion leads to multiple reflections then all reflections are taking into account to determine the clarity grade.
The nature
In some grading labs the distinction is made between internal and external characteristics. At HRD Antwerp grading lab all external characteristics are mentioned under polish grade, a part of the cut grade. This means that every defect induced by manufacturing of the diamond is not mentioned in the clarity grade. Other labs report internal and external characteristics in the clarity grade.
To classify the clarity grade a clarity grading scale is developed. All grading labs have created their own clarity scale and annotation. To give an example we show the two most common scales used by the labs working to the standards of the International Diamond Council (IDC) and GIA.
IDC Loupe clean (LC) VVS1 VVS2 VS1 VS2 SI1 SI2 PI PII PIII
GIA      FL    |     IF VVS1 VVS2 VS1 VS2 SI1 SI2 I1 I2 I3

The fourth C: Cut
The fourth C, the cut, describes the shape of the diamond and its proportions. The proportions of a given shape, mostly the brilliant shape, influence the optical performance of the diamond.
Let 's start with a rule of thumb that applies to all cuts, illustrated in the next pictures.
Example of to steep-to shallow-perfect
One of the main goals of the cut is to gather the incoming light and send it back to the observer. If the diamond is too shallow then the light returns next to the observers head. It creates a see trough effect and the brilliance is low. In a normal cut the diamond returns the incoming light mainly through the table, towards the observers head. The diamond looks bright and the brilliance is optimal. If the diamond is too steep then the light leaks through the pavilion. To the observer the diamond looks dark en dead. Of course there is a broad range of models and proportions. Besides common optical parameters as brilliance, fire and scintillation there is also a geographical and cultural difference. In Europe, HRD Antwerp was the first to introduce a complete diamond cut grading system for the brilliant shape. The proportions were divided in groups named "Very Good", "Good" and "Unusual". Next to the proportions they introduced a finish grade.  This finish grade was a mixture of evaluations concerning symmetry, polish and negative optical effects.
Fancy shapes collageOn the other side of the ocean, GIA created a cut description based on the "ideal" proportions, the ideal cut.
Special notice was given on the combination of the table size and the total depth. This was sufficient to remove too flat and too steep brilliants.
In 2005, GIA released a new cut grading system based on the optical performance of a diamond brilliant shape and an extensive survey. The proportions, symmetry and polish form together the overall cut grade ranging from Excellent to Poor.
In 2009 released HRD Antwerp a refined cut grading system that adds a top grade, Excellent, and some minor changes to the very good and good ranges. Together with the refined cut grade also the first objective Hearts and Arrows system was launched.
All other major labs have a comparable system to GIA or HRD Antwerp. The GIA system is best described as a grading on a stone by stone basis; the HRD Antwerp a grading based on areas of proportions.  The grading on a stone by stone basis has the advantage that the irregular formed proportion maps give a better match with the optical performance. For manufacturers it is more difficult to predict the end result during polishing. Systems with linear bounded areas of proportions are not as accurate near the boundaries.
Current research is situated in the field of fancy shapes. The labs try to translate the knowledge they gathered studying the brilliant shape to common fancy shapes like emerald, princess, marquise,... Currently the American Gem Society (AGS) is the only lab with a cut grading system for emerald and princess based on optical performance.
Diamond shapes
First there is the differentiation in shapes. Some shapes have a lot of brilliance, fire and scintillation (Brilliant, Flanders Brilliant, Princess, ...) other are less sparkling and show more stylish geometrical patterns (Emerald, Baguette, ...).The well known brilliant cut and its appearance is often used as a reference for existing and new cuts. Through its history WTOCD supported several new cuts. WTOCD was a co-designer of the Flanders Brilliant and gave technical and legal advice to many diamond designers. During the last couple of years it became clear to the diamond community that new cuts are a tool to boost their sales. The brilliant shape is an over defined commodity article which is very hard to brand. So in the next years people will see a lot of new fancy shapes appearing on the market. Let us hope that the claims they make are real and breathtaking...