Note: This is not an exact pattern, more of an explanation of the plan of construction. Experienced knitters will get this certainly, and novices will roll their eyes. Mitered square tutorial available here.
Side panel update here.
When I made the prototype Diamond Panel Jacket, I did it in separate fronts and back, sewing up the shoulders, joining the side panels (3 needle bind off) and then knitting the sleeves last, in the round.
Later I realized that I could knit the jacket seamlessly, without slits. That sounded much better to me.
To get there, one makes the front diamond panels and the back diamond panel first and then joins them at the shoulder with a quarter square triangle, picked up from the edges of the front and back panels.
To knit this shape, decreases are made at the center and both edges of the front side rows only. When only 5 sts remain, bind off. This produces a straight edge at the top of the shoulder, and nicely joins the front and back.
The diamonds and half diamonds are knit in a specific order, and of course if you are familiar with mitered squares or domino squares, you will recall that consecutive shapes are knit from stitches picked up from the previous shape.
See this post for side panel update.
NOTE: after making several of these jackets I changed the neckline a bit.
The neckline was too small and high in the original version, so I extended it a bit by adding two more triangles, a half-triangle ( A) and (B) a quarter triangle. Also notice that the back has changed too, ending in half triangles. The shoulders are the only seams.