**Some tiles associated with the 6th unit cubic Pisot number**

## I. Fractional
Symmetric Tiles

If the modifications of the grouped element technique are applied to one of
the order 5 asymmetric metasymmetric tiles, even though
it has no symmetries, a set of 32 attractors, including the original one, is
found, all of which have a similarity dimension of 2. 8 of these generate 6
partial postcomposition derivatives of the symmetric and demisymmetric
tiles, and one is disconnected, leaving 23 novel tiles.

Four of these tiles have similar outlines to the order 5 metasymmetric
tiles, though they contain voids.

Examination of the weight function suggests that 4 of these tiles make up a
symmetric tile. (Two copies - red and green on the
left above, and red and blue on the right above - have the outline of a
symmetric tile, and adding two more copies rotated by 180° fills in the voids.
They're not strictly quarters, as the 4 tiles come in two different sizes.)
This is confirmed by plotting the weight function for the unit cells.

The unit cells are as shown below.

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© 2015, 2016 Stewart R. Hinsley