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

## I. Compact
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.

Eight of these tiles have a fairly compact appearance, but 4 of them are partial postcomposition derivatives of the demisymmetric
tiles. The remaining 4 are shown below.

Four copies of these tiles combine to make a symmetric tile, so tilings of
these tiles have a multiple of four copies in the unit cell. (Dissecting one of
the four copies replaces one copy by five, so dissection doesn't result in
exceptions to this rule.)

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© 2015, 2016 Stewart R. Hinsley