NJAS>There's a much simpler question: what's the smallest number of pieces for dissecting a square into (pieces that can be rearranged to form) an equilateral triangle? 4 is possible - see http://oeis.org/A110312, especially the last link. 3 seems impossible, but is there a proof? The pieces must be bounded by simple curves. Neil What? No jhinged animation?-) Somewhat apropos: http://gosper.org/shardway.PNG (My G4G8(?) exchange gift.) --rwg On Thu, Sep 26, 2013 at 10:47 PM, Victor Miller <victorsmiller@gmail.com>wrote: Scott, this is discussed (rather tersely) here: http://www.ics.uci.edu/~eppstein/junkyard/cube-triangulation.html . Also, if you don't know about David Eppstein's Geometry Junkyard, you should. It's a treasure trove of all sorts of wonderful things: http://www.ics.uci.edu/~eppstein/junkyard Victor On Thu, Sep 26, 2013 at 8:51 PM, <rcs@xmission.com> wrote: This is from Scott Huddleston <scott.huddleston@intel.com> --Rich --- What's the minimum number of pieces for dissecting an n-cube into n-simplices? You can always dissect into n! simplices, but that's not minimal for n>2. This was an open problem when I was in grad school (awhile back). Is there always a minimal dissection that includes a maxvol simplex? - Scott