Some tiles associated with the 6th unit cubic Pisot number

Partial Postcomposition Tiles

II. Metademisymmetric Tiles

A 3 element tile potentially has 6 partial postautocomposition derivatives, 3 of order 5 and 3 of order 7. Thus the 2 demisymmetric tiles have between them 12 potential candidate attractors. However 5 of these are not connected, leaving 7 tiles - 4 order 5 tiles and 3 order 7 tiles.

All 4 order 5 tiles have the dissection polynomial c+2c2+c3+c4.

order 5 metademisymmetric tile order 5 metademisymmetric tile order 5 metademisymmetric tile order 5 metademisymmetric tile

The minimal unit cells (shown below) contain 4 copies of the tile, with signature 0011.

order 5 metademisymmetric tileorder 5 metademisymmetric tile order 5 metademisymmetric tileorder 5 metademisymmetric tile

There are 2 order 7 tiles with dissection polynomial 4c2+c3+2c4.

order 7 metademisymmetric tile order 7 metademisymmetric tile

The third order 7 tile has the dissection polynomial c+2c2+3c4+c6.

order 7 metademisymmetric tile

The minimal unit cells (shown below) contain 6 copies of the tile. The first two have signature 001111 and the last signature 001133.

order 7 metademisymmetric tileorder 7 metademisymmetric tileorder 7 metademisymmetric tile

© 2015, 2016, 2017 Stewart R. Hinsley