I’m working with a book on quilting called Hexagons, Diamonds, Triangles and More, by Kelly Ashton. It’s about using templates and jelly roll strips (and other strips of cloth in different sizes) to produce quilts and quilt blocks on the 60-degree angle — mostly triangles and hexagons, but also some other patterns. Some of the resulting piecework should really be assembled by hand rather than machine. The bits of cloth are too small to be easily machined together; hand stitching may be required. 

Um. No.
There are limits to what I am willing to do for a commercial quilt. This may be one of those things. In essence, though, the process is the same as it is for English paper piecing: cut out a group of pieces of fabric using a template. Do this by cutting up a plastic milk carton into a number of durable template parts, and then using a ruler and rotary cutter to slice through dozens of pieces of fabric at once. Then you will have enough pieces to work with, to build up larger structures. I chose to start by working with the flat triangle shape. This gets cut out of a strip of cloth about 1.75″ wide; I chose to use two gray fabrics and a black fabric. For this next quilt I want to have the geometry provide the visual interest, and let the color palette take a back seat to the design. That’s the intention, in any case. As you can see, I made up a number of templates all at once. This quilt is going to be triangle-heavy, but with a range of triangular shapes and structures that also rely on hexagons (because a hexagon is six triangles). These three shapes are symmetrical, which means they can be stacked in useful ways. I can either assemble them into strips as shown in the first photograph. Or I can assemble them into pyramids. Emergent properties of course become obvious once you lay out a number of pieces for sewing. Triangles oriented in a particular way become six-pointed stars. It’s worth noting that the template must have a seam allowance. Here I’ve got a 1/4″ seam allowance on the template piece, and so the layout has this weird hole in the middle when the pieces are aligned but not yet sewn together. 
But that hole disappears eventually. I am not yet skilled at sewingvthe central gap together. but a straight-line technique does not appear to work correctly. The work needs a little more finesse than that.

What’s really elegant here is that the templates in the book are intended to work together. So the finished triangles now woven/sewn into this hexagon are the same size as the triangle templates. Which means that if I finish the pieces I’ve cut into three full stars, I can then put those stars almost like appliqué structure into a quilt that is otherwise constructed of triangles. 

F. Buckminster Fuller devised a three-point grid rather than the Cartesian grid of squares that we use in modern mathematics.  It’s funny to discover that Midwesterner’s grid system underlying the designs of four-hundred-year-old quilt patterns. One wonders what he was sleeping under, growing up, and what dreams those blankets may have inspired.