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We will model a round diamond from scratch and all you need is some sort of vertex modeler - my personal favorite workspace is Carrara Studio, but the concepts of this tutorial are not application dependent.
After researching some diamond cuts I found that the round diamond is by far the easiest cut of diamond to model - simply because the diamond layout consists basically of the geometry of a circle and two squares.
So first, in your vertex modeler - use a predefined oval or circle object to create a circle with 16 sides and a scale setting of 10“ in Carrara or 1.00 in another modeler. This circle should be centered around the origin [x=0, y=0, z=0] to make orienting the next step easier.
Create a square lying on the circle with sides at 50% of the circle - here they are set to 5” in Carrara or .50 in another modeler. This square should also be centered on the origin
We will now rotate this square 45 degrees by reassigning the coordinates to the vertices (or you can do this using a rotation tool - but I found it easier just to use the coordinates) and will set the points on the square to:
Top vertex: [x=-3.5, y=0, z=0]
Right vertex: [x=0, y=3.5, z=0]
Bottom vertex: [x=3.5, y=0, z=0]
Left vertex: [x=0, y=-3.5, z=0]
Having rotated our original square we will insert a second square exactly as we did in the last step, centered on the origin.
We will need to weld these two square together and to do so we will need to add vertices on the intersection points of these two squares. Use your add vertices tool to place new vertices on your second square at the points where they intersect your first square.
Select your first square (the rotated one) and do the same on its edges. Note that these vertices that you place on your rotated square will be exactly on top of the vertices of intersection you just placed in the last step.
We will now weld the intersecting vertices of the two square together by selecting each PAIR of intersecting vertices (one from the rotated square, one from the second square - note that they will visually look like one vertex) and using a weld tool, combine these two vertices. (In Carrara the weld tool is in Selection > Weld or Control+Shift+W)
Repeat this step for all eight intersecting vertex pairs on the squares.
Next we will link the 16 points on our combined square to the 16 corresponding points on our circle. To do so select the vertex on the square and the corresponding vertex on the circle and as per the above image, link the vertices two at a time using your link tool. (In Carrara the link tool is in Selection > Link or Control+Shift+L)
After you have completed welding the 8 vertices on the squares and have linked the 16 vertices on the circle to the squares you are now ready to move from 2D to 3D. Select your squares as shown in the image above, and switching to a better perspective move your selection vertically on the Z axis. If you have linked and welded correctly your lines to your circle should stretch down as shown above. Adjust the height of the squares above your circle according to the shape of the diamond you wish to achieve.
Next insert a vertex at a point somewhere on the negative z axis as centered on the origin (ex. [x=0, y=0, z=-7]. This will serve as the bottom point of your diamond.
At this point, select your circle vertices and empty the polygon as we will need to fill in its sides later. (In Carrara this is located in Selection > Empty Polygon or Control+Shift+F)
Using the same technique as you did when linking your squares to the circle, link the bottom vertex that you have created with the 16 vertices of your circle as shown in the image above.
After you have created your diamond wireframe, first fill the middle section of your diamond by selecting the quadrilateral sections four vertices at a time and using the fill tool to fill thier plane in. (In Carrara, make your selection and then select Selection > Fill Polygon or Control+F)
Finally repeat the fill step and select your bottom vertex and the 16 vertices on your circle to complete the diamond.
This should be your completed wireframe model of your diamond! You can now texture, export, and render your flawless creation!
Some notes on rendering:
After you have textured your diamond place many spot lights in multiple angles around the diamond for maximal lighting, reflection, and refraction effects.
The above image was rendered in Carrara Studio 1.1 which does not support caustics (which account for the internal reflection of light within the object) so you don't get the cool effect of the diamond shimmering with light. However if you render this in Carrara Studio 3 or Bryce or some other program that does support caustics your results should be more like this sample image at Eovia:
(Note that the model you just made is identical to their diamond models!)