This page covers rep-3 tiles which are not included within any other pages. It is likely that further investigation will identify such figures as members of defined classes of rep-tiles, and that they will be moved to corresponding pages.
A: The figure shown below has vectors joining elements of (1,0) and ((3½.cosa)/2, (3½.sina)/2), where a is the same as for the z1-homeolineotrimer. This figure seems to refute the conjecture that all homeopolymers have one copy in the unit cell, the tiling being identified have two copies in the unit cell, with a displacement vector (0.5,0). The tiling vectors are (1+(3½.cosa)/2,(3½.sina)/2) and (1.5+(3½.coa)/2,-(3½.sina)/2). If the original vectors are rewritten as (1,0) and (c,s) then the tileing vectors are (1+c,s) and (1.5+c,-s).
This construction does not generate rep-tiles for most other angles, but it is suspected that there is a rep-tile with this construction corresponding to the z-2-homeolineotrimer.
data file angletrimer.xil; images generated at 6x5 per screen at 1280x1024
B: R. William Gosper documents a rep-3 tile at http://www.ippi.com/rwg/Bodhi.htm. I have yet to reverse engineer this.
C: Walter Schraa documents 6 rep-3 tiles at http://www.xs4all.nl/~wolter/ws_page4.html. These include the cis-fudgeflake, terdragon and both demiterdragons, as well as the double cis-fudgeflake.
© 2001 Stewart R. Hinsley