sharkee and Juliea9967 - my avatar is the diamond log cabin star, i.e. a log cabin quilt that's built around a diamond shape. When I made the first one I was asked by so many members of the board to write a pattern that I did that, and I am selling it on the board. The pattern quilt has plain corners rather than the radiating design. All the information is here:
http://www.quiltingboard.com/t-41448-1.htm
Pictures of this and the other diamond log cabin star quilts are in these posts:
http://www.quiltingboard.com/t-26643-1.htm
http://www.quiltingboard.com/t-41449-1.htm
http://www.quiltingboard.com/t-55682-1.htm
And no, it isn't paper pieced.
Lots of people have referred to having wonky blocks in their log cabins. There are ways to avoid that. When I started quilting, I read Judy Martin's log cabin book and employed her techniques for several log cabin quilts. Judy's book teaches you to use the length of grain when possible, use starch, cut the logs to size before sewing, press without distortion, sew carefully, and measure often. A log cabin is not a complicated block, but it does have a lot of pieces.
I use PP for snail's trail, square in square, and certainly for designs with really narrow angles. But I don't want to be limited to PP to get some kind of accuracy. For a block that has reasonable angles, I look at PP as a kind of crutch, sometimes necessary but if you use it all the time you will forget how to get along without it. A log cabin block is very achievable without PP if you use a good technique. (I haven't tried 1/4" logs yet, so you may be right about using PP for that.)
Oh - forgot to say that I did PP the border in my avatar.