A t-polymer is a polymer with a similarity dimension of 2, in which 3 components have a common centre. Clearly a t-polymer requires a 'cinch point' at its center. Hence it is not possible for there to be a t-trimer. There are 10 t-tetramers, 2 of which are mirror-symmetric. It is not possible to create other t-polymers by extending the 'tail', because the contraction must be 1/(n-2), which only matches the contraction for a 2D fractal when n=4. I conjecture that there are no other t-polymers
Consider the case when 2 components are positioned parallel to the long axis, and 2 components are positioned perpendicular to that axis. There are two possibilities - either the two perpendicularly-positioned components are rotated by 90° and 270°, or both are rotated by 90°, one being first reflected in the long axis. (If both are rotated by 270° then mirror images of the latter are generated). In the first case symmetry means that reflection of any component about its long axis has no symmetry. There are 4 possibilities - each of the parallel-positioned components can be orientated in the same way as the overall figure, or rotated by 180°. The two cases where the orientation of these two components differ have the perpendicularly-positioned components overlapping, and hence a non-uniform measure, so for the first case there are 2 polymers
Both these figures tile the plane (each can be combined with its mirror image) to form a double square, which obviously tiles the plane. Therefore they are rep-tiles. The body (leftmost 3 components) is circumscribed by a square. The area of the whole figure is the same as that of that square.
In the case when the perpendicularly-positioned components are rotated by 90° (one first reflected in the long axis) there are 16 possible figures (each of the parallel-positioned components can be rotated by 0° or 180°, and reflected in the long axis, or not). As above those figures where the parallel-positioned components are rotated by different angles have a non-uniform measure. Thus there are 8 t-tetramers of this form.
These also tile the plane, but 4 copies (figure, mirror image, figure rotated 180° and mirror image rotated 180°) are required.
When the two components aligned parallel to the long axis are included amongst the 3 components having a common centre the resulting attractor is disconnected. For the attractor to have a uniform measure (non-overlapping components) the components aligned parallel to the long axis must be rotated 180° with respect to each other. This reduces the number of potential attractors with a uniform measure to 32. Of these 16 (those in which the other two components are either similarly orientated, or reflected in the long axis and rotated by 180° with respect to each other) actually have a uniform measure. In the case of the 8 in which the two components aligned perpendicularly to the long axis have the same orientation the two components aligned parallel to the long axis form a disquare, irrespective of the choice of their individual orientation, so the number of distinct attractors, ignoring internal structure, is reduced to 4, which form 2 mirror image pairs.
Both of these tile the plane, the figure being combined with itself to form a disquare.
The other 8 possibilities give rise to 4 mirror image pairs.
These also tile the plane. 4 copies are required to form a disquare. A partial image of the tiling of the first is shown below.
Source: The stingray fractal (t-0,0,90,270-tetramer) was stumbled across while investigating the terdragon and other 3-part IFSs with a similarity dimension of 2. The remainder were discovered by a systematic investigation based on the first.