Polyhexes are a beautiful thing

Polyhexes are like polyominoes but made up of hexagons instead. These are activities about these very tessellatable, rotatable and flippable shapes!

Challenge On Boarding – How to make a polyhex

Find the smaller polyhexes by colouring in hexagons that are joined together.

How many can you find that have less than 5 hexagons?

Challenge On Boarding – Getting to know polyominoes

Naming Polyominoes

  • Names are based on the number of squares.
  • 1 – monohex, 2 – dihex, 3 – trihex, 4 – tetrahex, 5 – pentahex, 6 – hexahex etc.
  • They have similar naming conventions to polygons after 4 i.e. pentagon, hexagon, heptagon, octagon

Challenge On Boarding – Testing for symmetry

Rotational Symmetry

  • Cut out a polyhex that you want to test
  • Draw an outline of the shape
  • Place a cross on the one of the hexagons and the on the same place on the outline
  • Rotate the shape until the cross on the shape gets back to the cross on the outline
  • Did the shape match the outline at any time on the way round?  If it did, it has rotational symmetry

Reflectional Symmetry

  • Cut out the polyhex that you want to test
  • If it has reflectional symmetry, there will be a line that goes right down the middle.
  • To test a line, fold the shape down that line.
  • If both halves of the shape match, it has reflectional symmetry.
  • Alternatively, you could draw an outline and flip it over
  • If you can find a way to flip it so it matches, it’s symmetrical

Challenge 1 – Find pentominoes with rotational symmetry

Find 20 polyhexes that have symmetry.

Can you do this with polyhexes that have less than 100 hexagons in total between them?

Challenge 2 – Play Kajitsu

This type of puzzle created by from the MathPickle website where there are lots Kajitsu puzzles not to mention all the other types of puzzles (or pickles). 

Download or share all of these challenges with this pdf and let us know how you got on with it by tweeting using #momentofmaths and start to see Every moment is a #momentofmaths.

If you like this challenge, you should try Rotating Polyominoes too.

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