When is an Octagon not an Octagon?

This sweet octagon motif is in my book, Go Crochet! Afghan Design Workbook.  I just love it.  I may re-make it soon and blog post about it.  I was thinking that I needed another octagon. I was thinking that I wanted something somewhat open and not too solid. I was thinking that post stitches would add depth and texture.  I know it may not look like an octagon, because it doesn't have any sides at all, let alone EIGHT of them.  But can you see it? 

When you join a floral style motif like this one, it will join to its neighbor at the purple dots.
If you draw imaginary lines from purple dot to purple dot... you'll see the 8 sides of the octagon. If you were to make this into a "join as you go" motif, I would likely use my favorite technique... a chain space.  It looks like there may be 9 dc on each "side" or petal.  I would likely change that to be (4 dc, ch 3, 4 dc) instead of doing 9 dc.  Then when you join the finished first motif to the subsequent motifs, you can join with (4 dc, ch 1, sl st in ch-3 sp of First motif, ch 1, 4 dc) on the final round. My point is... you can turn ANY motif into a "join as you go" motif.  (BTW, 'join as you go' means no sewing. While you are working the final round of the motif, you are finishing the final round at the same time you are joining it to the other motifs, so that when you finish the motif, it is already joined. A dream come true for those who don't like to sew.)  Don't like ends? Make it one color instead of 3, that will dramatically reduced the number of ends (by 2/3rds in fact! 66.6%). 

Octagons though, don't TILE or to use the math term 'tesselate' or become a 'tessellation'. If you put a bunch of octagons next to each other matching sides as if to make a tile floor of octagons... you can't do it without leaving some blank holes.  Matter of fact, you'll get a SQUARE shaped hole where the octagons don't meet up.  This is why Octagons and squares are friends. Pick any one of the 10 squares in my book to be friends with any one of the 10 octagons.  You may need to use the 'join as you go' modification on a couple, but that's not a big deal, I just told you how to do it!