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Hearts and Arrows

Formation of the Hearts and Arrows patterns
Every polisher knows that polishing Hearts and Arrows by HRD Antwerp is not easy. Some knowledge about the optical formation of both the hearts and the arrows can ease the job. This article reveals the exact interaction between the facets and the heart and arrows pattern. The polishing sequence of the facets used in this article is not exclusive. There are other polishing schemes possible to create a Heart and Arrows brilliant. The sequence demonstrates the exact number of facets needed to form one heart and one arrow. Pavilion main facets are coded as Pm(index), pavilion halve facets as Ph(index). Crown main facets are coded as Cm(index) and star facets as Cs(index).
Forming the hearts
Hearts: step 0 Each heart is formed by several facets. The structured light is entering the diamond and the diamond facets start to interact with each other creating optical effects. The slightest faceting error in depth, angle or azimuth can lead to deformed heart patterns. The heart patterns are created mainly by the pavilion main and half facets. Let's take a look at the formation of the heart patterns. First the creation of perfect symmetrical hearts is explained. In a next article some examples of common polishing errors together with their influence on the heart pattern are given.
A perfectly preprocessed diamond, 8 main crown facets and 8 main pavilion facets, shows no hearts and no arrows (figure 1). A perfect round girdle is assumed. The first pavilion half, Ph1, gives birth to one of the two lobs of the first heart. The result of this first step, when viewed through a H&A viewer, is illustrated in figure 2. On the opposite side the white triangular shaped polygon forms a half of the v-shape of the fourth heart. The formation proceeds with the following pavilion half resulting in Figure 3.  The second lob of the first heart is getting shaped. As in step 1, polishing
Hearts: step 2 Hearts: step 3
Hearts; step 4 Hearts: step 5
this facet gives rise to the other part of the v-shape of the sixth heart. To create the first complete heart, the opposite halves Ph9 and Ph10 need to be polished. Remember that the goal of this article is to describe the formation of one heart and not to start a discussion on the normal polishing sequence.
Besides creating the basic shape of the fourth heart they reveal a subtle effect on the shape of the opposite heart. A small gap is created between the hearts and the edge between the halves and the pavilions (Figure 5).  The next stage in the process is how to form the v-shape on the first heart. To achieve this proceed with another two halves, Ph8 and Ph11 and investigate how they influence the patterns. At this stage the heart pattern is almost complete (figure 7 and 8). To flatten the shoulders of the heart the star facets are being polished. The result of this action is illustrated in
Hearts:step 6 Hearts: step 7
Hearts: step 8 Hearts: step 9

figure 9. It is amazing but it requires TEN pavilion facets and TWO crown facets to create one complete heart pattern. The two crown facets, the table and the star facet opposite to the heart, form the shoulders of the heart. The pictures show that while polishing the necessary facets to create the first heart also several parts of the other hearts are created. This makes it extremely difficult to correct or adjust the heart shape after polishing.
Forming the arrows
Arrows : start shape Similar to the creation of the hearts, also, every arrow is formed by several facets. Exactly how many facets are needed to form at least one complete arrow?  Let's investigate the formation of an arrow. In figure 10 the start state with 8 bezels and 8 pavilion main facets is shown, when looking perpendicular through the table. Again the assumption is made that the girdle is a perfectly round girdle. We start with polishing the first pavilion half facet, ph1. The result of this action is visualized in figure 11.Each pavilion half facet has an impact on the arrow above and the arrow opposite to this. Figure 12 shows the effect of polishing the next half, ph2. This creates the biggest part of the arrow head and the rough shape of the arrow shaft. In figure 13 and 14 the opposite halves, ph9 and ph10 are polished. The result of this action is a reshaped, smaller, arrow shaft. Finalizing the first arrow requires the polishing of the crown star facets. Figure 15 illustrates the effect of the creation of the first star facet, Cs1. The star facets cut off the arrow point from the shaft and start forming the star shaped inner pattern round the center of the diamond.
Arrows: step1 Arrows: step 2
Arrows: step 3 Arrows: step 4
Figure 16 shows the effect of the next star facet, Cs2 being polished. The first and the second arrow are formed. It is impossible to create one full arrow pattern without creating the opposite at the same time. Completing the third and fourth star facets, Cs5 and Cs6 creates the first two complete arrows, shown in figure 17 and 18. SIX pavilion facets and SIX crown facets (table, bezel, four star facets) were required to create one full arrow.
Arrows: step 5 Arrows: step 6
Arrows: step 7 Arrows: step 8
Doing so, the opposite arrow is also completed. The tricky part in polishing a true H&A is that the same facets are involved in both the creation of the heart pattern and the arrow pattern. Every error influences several H&A patterns at the same time.
General Conclusion
Every H&A pattern is created by several facets. In descending order of importance, the most important facets are:
- The pavilion main facets
- The pavilion halve facets
- The table
- The crown main facets
- The star facets
The crown half facets only influence the surrounding circular band close to the girdle. The correct proportions are discussed in a previous article: “Hearts and Arrows by HRD Antwerp - Relationship with the cut parameters”. The next article will give more information on the influence of facet position and orientation errors on the hearts and arrows patterns.