it's clear that it's a
  container, it's pretty much flat, and it's decorative. Is that all? I have
  the following questions regarding tato:
  1. Does a tato closes over its center or do they sometimes also close by
  one of its edges for example?
  2. Is a tato folded from a regular polygon (square, pentagon, hexagon,
  etc.) or are they sometimes folded from rectangles or equilateral straight
  triangles?
  3. Is a tato's resulting shape that of a regular polygon or do they
  sometimes end up with sides of different lengths?
  4. Is a tato simetrical, being its right half a mirror image of what's in
  its left half, or are they sometimes asimetrical?
  5. To open a tato do you pull opposite flaps or tips or can you sometimes
  open it by pulling a single flap or tip?
  Can you please help me by answering those five questions? That way I can
  have a better idea to propose for the challenge.


I believe if you read further, David Lister’s article answers some of the tato 
questions you posed
(  http://www.britishorigami.info/academic/lister/tato_folds.php  )
Also, have you looked into kamon-ori? It m a y  be a name that differentiates 
the pinwheel type tato.
OriFUN to all,
Dianne

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