Further Questions about Tetrads
9. Which tetrads are shown in Gardner's book?

At the end of 1979 I was able to improve the solution of another puzzle presented by Martin Gardner. The challenge was to pack n unit squares into one square with minimum side length. Now it was time to write a letter to Martin Gardner and I included a few tetrads. Here is his answer.

      Martin Gardner forgot both improvements.

The first edition of his book 'Penrose tiles to trapdoor ciphers' appeared 1989. The tetrads of Scott Kim were presented in the same way as in Scientific American. In the addendum to this chapter the polyamond tetrad of Ammann, Frederickson and Loyer is shown. I had expected that my tetrads would also be mentioned in the addendum.
Later I purchased a revised edition printed in 1997. This edition has a postscript where four of my tetrads and one from Karl Scherer are mentioned.
Gardner writes: 'In discussing Scott Kim's tetrads I said it was not known if one existed with polygons of order less than 12. Walter Trump, of West Germany, answered yes with the order-11 polyomino shown in Figure 3. Trump also sent the tetrad of congruent hexagons (Figure 4) which has the property that any pair of hexagons will form a square.
Figure 5 shows Trump's two-hole tetrad made with polygons that are bilaterally symmetric in two directions, and having a border with the symmetry of an equilateral triangle. Figure 6 shows his tetrad without holes, made of bilaterally symmetric polygons. This pattern was independently sent by Karl Scherer, also of West Germany.

      Now it would have been nice to see the Figures 3, 4, 5 and 6. But the last printed Figure of the postscript is Figure 2.

This year (2020) my friend William Walkington found in the internet a version of the book where all Figures can be seen. I present them here as vector graphics.
Figures 3 and 4 are also printed in the book of Heinrich Hemme. [5]

Figure 3

Figure 4

Figure 5

Figure 6
   Polyominoes of order 48

Meanwhile, the tetrad of Figure 6 was improved by Frank Rubin and Karl Scherer. [6],[7],[10],[12]

      Polyominoes of order 34

Construction of Figure 5

1. Draw 7 unit circles in order to construct the inner polygon.

2. Reflect the green points through the dashed blue line in order to achieve the yellow points and one other polygon.

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 Walter Trump, Nürnberg, Germany, ms(at)trump.de, © 2020-02-12 (last modified: 2020-02-12)