The old fashioned traditional kaleidoscope block is eight 45 degree triangles pieced together with 4 triangle units sewn to the corners to make the square block. I recently completed 90 spiderweb blocks to make 3 quilts. spiderwebs are also eight 45 degree triangles but the triangle units are cut from strip sets. Here are the best tricks I learned when sewing the blocks together.
1. Invest in the 45 degree ruler! definitely worth it IMHO. Creative grids is very nice.
2. When you join the two halves, pin or glue well (I pin) the center part where it all meets. I like to pin because then I can make sure I am intersecting the "x" of seam lines on both units. On my first pin I put it in intersecting the "x" checking to make sure I am dead center on both halves, leaving it straight up and down through the intersection. Then I insert 3 more pins before removing the one that is straight up and down.
3. Start sewing from the center out. You have to remove the block and flip it to sew the other half but it really helps the intersection of the 8 points and as an added bonus, by starting from the center it allows you to furl the center seams out like a windmill so you don't get all the bulk and you don't have to press all your seams open.