Flexomino Puzzles

All images and Flexomino Š Abaroth, 2013. Permission is given to reproduce for non-profit purposes only.

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I recently found this article on the blog of Alexandre Muņiz: Flexible polyrhombs.

Here is the image he posted of a figure with 5-fold symmetry.

 

   This can be viewed as a construction of pentominoes on 5 angled planes, with the pieces allowed to "flex" across the joints. I coined the name "Flexominoes" for puzzles of this type. Almost immediately, I wondered if I could complete the star shape above using the 5 tetromino pieces, and found that that I could. I also found several more patterns with rotational symmetry before discovering other possibilities using this new topology.

Hover over an image to see a solution.

Tetra- and pentaflexominoes with 5-fold symmetry
   
  The star that led to a whole new galaxy of possibilities  
When I found this solution ... ... I realised I could "fold" the outer pieces to make ... ... a more pleasing shape.

 

The drawback with these extra folds, is that it becomes ambiguous as to which of the flexomino shapes make up the "corners".

So, I will post both versions for any other patterns which make use of these extra folds, and include an arrow icon in the altered version.

   

George Sicherman pointed out that a 13th pentomino can logically be added, which is consistent with the topology - a star shape which can only ever be placed at the central nexus of a 5-fold symmetric construction. This is not necessarily at the centre of the pattern, but the point where the 5 planes meet. The same logic would apply to adding a 6-pointed star to hexflexomino patterns with 6-fold symmetry, etc. George also found 2 other pieces that can only be placed at the nexus, but when "flattened" they both look exactly like the "P" pentomino, but are topologically distinct. I would prefer not to use them myself, but knowing of their existence may prove useful.

     

 

 

Pentaflexominoes with 3-fold symmetry
    This one is also an impossible object !
     

 

Pentaflexominoes with 6-fold symmetry
     

 

 

Tetra- and pentaflexominoes with 8-fold symmetry
    Non-ambiguous version found by Alexandre Muņiz
     

 

 

Penta -and hexaflexominoes with 5-fold symmetry
     

 

Penta- and hexaflexominoes with 6-fold symmetry
   
     
     

More Flexomino Puzzles

 

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