They could also be set together with diamonds which would make it really cool. I think I would have to hand piece if I did this, but a really effective look.

F&P have a pattern with the striped triangles sewn into a hex, but spinning, and solid tris at two opposite ends to make a row...I have one I made, folded in the "to be quilted" box....but I cannot remember the name.....maybe someone else does. I do remember as I was peicing it, how easy it was.....

Thanks to everyone for instructions and suggestions. Since I don't have the blue or pink solids, I could forego using those and assemble these as non-stars, I suppose. Decisions, decisions! The fabrics are just lovely; I should spread the pieced triangles out and take a photo so you can all see. And because they were lovingly made by someone else, I feel an obligation to treat them in the best way possible......if I only knew what that was! LOL

You've all been so helpful. I appreciate your comments and ideas very much.

Jaybird patterns have great patterns that uses these triangle

Look at your blocks as if it was one central hexagon (white) surrounded by six Petals that look like a cut diamond. The name of the block is 'Texas Star Flower', an early American pattern. Here is a link to a blog that shows how it is laid out, http://gwensquiltbarn.blogspot.com/2...-quilt_19.html
When you think of your quilt in term of HEXAGONS, you will find a very pleasing arrangement, like Grandmother's Flower Garden quilts. As for your need for more solid pink and solid blue Triangles, I recommend that instead of trying (in frustration) to match the pink perfectly, think in terms of Pinks (plural) and Blues (Plural) Select new yardage in three tones, so you have three pinks that ALMOST match, and three Blues that are close in color, then you can mix them up and not feel uneasy, it will look as if you WANTED it that way. I'm eager to see your finished project. You have a treasure there.

I think these blocks were made with the intention of putting hexagons between them.

Thank you for this! And yes, I had thought I wouldn't try to match the solids but get others in the same tone. Also, the pieced triangles include prints in these colors: pink, blue, yellow, green, purple, red, so I thought I might find solids in all those colors, which I think would make it look like a flower garden. Choosing triangles for each "block" will be my biggest issue because I get hung up on all the different options. But these fabrics are just charming! I've said that, I know, but I sorted them today and I keep being delighted by them.

I would if I could not join them in anyway, you might think about sewing them down a on a fabric in a picture type quilt or wall hanging,etc.

Anxious to see what you design!

so many options for finishing these wonderful blocks. My thought would be to take the pink & blue off & add a two inch whits strip around all the blocks & then sew them together. You would have to do a Y seam to attach them, but there are many tuts on how to do them. Kaye Wood has a easy way to do them.