I think Paperprincess is right! That would be my guess as well.

my guess as well.

Is the first one hearts and gizzards?

I don't know this pattern or if this suggestion is right, but I had the Nebraska Quilt Museum help me identify the quilt pattern my grandmother used in 1935.
I found them online, sent them an email and got a response back pretty quickly.

Here's a screen shot of the google search.

The pattern of the first quilt is known as Star of the West or Star Cresent according to my book. Very pretty.

That first quilt is a variation of the Hearts and Gizzards pattern. The hexies are very interesting. I would agree with others who think it was meant to be appliqued to a background fabric. I guess that is one we will never know for sure!

With those hexies... I'd snip them apart at the points holding the rows together, then slide the alternate rows over so the top of the hexies fill in the diamond space above them, and sew them together that way. Then you'd have a solid top.

Very interesting pieces.

The diamond shapes are integral to the design, and used to be called the garden path between the hexie circles. You will have to cut some and stitch them in the empty spaces. Look at pictures of antique quilts for inspiration. By the way, the diamonds were green to represent a path.

That would be my thoughts too.