You will not lop off any points. I've made Bonnie Hunter's Spider Web, which is constructed exactly the same way. The only change is that for the Spider web, you are sewing multiple strips of varying color/width onto the original piece - the one that was cut using the template. In "Periwinkle" you place the template cut piece (color) and then the chunk of white.
Think of a square, cut in half diagonally. At the point across from the longest side of the resulting triangle, lay down your "kite" piece (This is the template cut piece. If you are making any number, I would suggest either purchasing the template available from MS, or print Bonnie's off and take it to a glass shop to request that they make an acrylic template for you. At the Bonnie Hunter class I took in DE last year, the coordinator had several of these made up for those who wanted to purchase them; I think they were about $2 each.)
So you've got that kite piece the the shorter point at the tip of the triangle point. Now add your white piece, flip it back and press, then trim to the paper foundation (the foundation is called Wacky Web paper @ MS, or again, if you go to quiltville.com, you can find directions for easily making the paper foundation from doodle pads - which is what I used - or recycled copy paper, etc. ). You will have a colored section in the center, with the long tip of the kite 1/4" from the longest side of the triangle; the white pieces would be the triangles on either side of that, and filling in the other two side triangles that make up the larger triangle/