I may be wrong here, but I thought the kaleidoscope block was made up of 45 degree triangles - thus making making an octagon w/HST at four corners to make a square block. I did make one a long time ago, so I may be getting triangles confused here......or maybe there are now variation of that block....
OMgoodness, you are absolutely correct. don't know what I was thinking when I said Kaledioscope left as a hexi. The spiderweb and kaleidoscope blocks are indeed 45 degree angles and form and octagon and what the OP linked to is a 60 degree angle. Wow, I am starting to scare myself with all the mistakes, typos and forgetfulness I have had lately.