You can see from the schematic below that a half hexagon shawl consists of 3 triangles:
The schematic shows where the shawl is cast on. Most of my half hexagon shawls start with approximately 9 stitches cast on. Increases are then made along the edges and either side of two increases lines.
Charts for this type of shawl would look like this:
The columns with the red border is the 'spine' stitch. Remember we had one 'spine stitch' in the top down triangular shawl? In a half hexagon shawl we have two spine stitches.
The charts for this type of shawl is three triangles next to each other separated by a 'spine' column. Charting out the full width of the chart takes up a lot of space in a pattern, so to save space I only chart one of the triangles:
I would write the instructions like this:
Row 1: k2, work chart, k1, work chart, k1, work chart, k2.
Row 2; k2, p to last 2 sts, k2.
You can take a triangular shawl and add a spine stitch and another triangle and you get a half hexagon shawl. Understanding this makes it easy to convert a half hexagon shawl to a triangular shawl or a triangular shawl to a half hexagon shawl.
This is another shape of shawl that I really like. It starts out like a half hexagon shawl but after a few inches the increases for the central triangle stops and the side triangles continue to increase like normal. The schematic below is for The Frosty Diamonds Shawelette and illustrates how this type of shawl is constructed.
In the picture below you can see what it looks like when the increases for the centre triangle stop: