The Elusive 13 Piece Complete Set Puzzle

At the 13th gathering for (Martin) Gardner my gift exchange was a set of 13 pieces that can be assembled into many shapes in many ways.

For this project I wanted to design a complete set puzzle with 13 pieces (to match the number 13 of the conference). It turned out that complete set puzzles with 13 pieces are very rare. I found precisely one; so that is the one I used.

At G4G13 I was also allowed to present this project in a 5-minute presentation which will probably appear on youtube when the organisers have finished editing all contributions. When that happens I will update this page with a link to that movie.
the 13 different pieces

My PERL program that enumerates all possible regular N-sided polygons with K different edge styles can be downloaded here. To run it you will need a computer with the PERL programming language installed.
The codes for this puzzle are generated with the command 6 2 01
The first argument is the number of edges of the polygon (6), the second argument the number of edge styles (2). The last argument describes what happens to an edge when it is flipped. In this case an edge of style 0 is mapped to itself and also an edge of style 1 is mapped to itself.
The output if the program is very verbose. The source code is pretty well documented. The code is not very efficient; for this project readability of the source code was much more important than execution time. The list that defines the 13 shapes in the set appears at the end of the output.

Example solutions for the outlines in the challenge sheet

This solution is one of the 12 that have congruent holes; these holes are shown in light Violet. Solution of challenge with three holes
Sample solution for the kite shape.
The catch with this puzzle is that, in order to fill the given outline, you will have to leave a hole in the shape of two connected tabs, shown in Violet. Simple counting of the number of tabs and slots needed to fill this outline should have informed the observant puzzler. If you wasted a lot of time not knowing this, you will now probably hate me. Get over it.
Solution of kite-shaped challenge
Sample solution for the oval shape.
The catch with this puzzle is the same as with the kite shape. You were warned.
Solution of oval-shaped challenge
Sample solution for the hardest shape.
The catch with this puzzle is the same as with the kite and the oval shapes. You should not ignore warnings from puzzlers.
The double tab hole appears at the same place for all five solutions.
Solution of hardest shape challenge