In 2001 Roel Huisman suggested a set of polyforms made up of a square, a sliced square (tan) and a sliced domino (dom). There are 32 two-sided pieces and some constructions with this set are shown on Roel's site. and on The Poly Pages. Since all pieces are asymmetric we get 64 pieces if we consider the one-sided pieces. This set can cover an area of size 160 and a lot of new constructions are shown here. But first let's have a look at the original set.

The first problem in 2001 was a dissection of a 5x16 rectangle. Handsolving is very hard with this set and therefore I modified an existing program to work with sliced pieces. This way many constructions of rectangles, parallelograms, trapezia and multiple shapes were found. On the 6th of Februrary in 2001, I started to make quadruplications of the pentominoes and the last replica of the X-pento was found on the 26th of March in 2001.

Now, in 2006 with computers much faster and programs slightly better all twelve replicas were found in about one an hour. Especially splitting the X in two fixed parts saved much computer time.

I had another look at convex polygons with two lines of symmetry. We can get polygons with 4, 6, 8, 10 or 12 corners and even the square of size 4sqrt(5) which was hard to solve five years ago doesn't take much time now. The dodecagon with rotational symmetry seems to be the polygon with minimum perimeter.

There are some figures with pentomino shaped holes at roel's site and I tried to solve all cases.

It's also possible to make 10x10 squares with pentomino shaped parts uncovered. Unfortunately the uncovered parts cannot be totally enclosed .

Beside the 9x9 square with an 1x1 hole, which I found in 2001, a new similar hole figure with a tilted square is shown. Even now this was rather hard to find.

Since there are only asymmetric pieces in the two-sided set, the one-sided set is suitable to get

Those constructions are no real challenge since essentially the two-sided set is used. But if you are looking for

After this work was finished a new problem arose. Is it possible to make

At last I tried to replicate all

As the picture shows many symmetric decominoes are a combination of two pentominoes. For the remaining pieces I split the whole piece in one or two pairs of symmetric parts and solved half the shape with the two-sided set. Two examples are shown, all solutions are here ..

This strategy failed for the red colored pieces and a special search for each shape was neccessary. Using some parts of existing constructions reduced the time needed. Two examples are shown, all solutions are here .

Don't know when I feel like solving the missing 1006 problems.

To display some of the constructions I sawed the pieces, attached little magnets on the backside and put the pieced on an iron board.

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