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Introduction

      The pieces of the Crab are soft diamonds ; it may be necessary to specify what I call a soft diamond ; on the figure below, we see, on the left, a traditional diamond ABCD ; in the middle, we see that the segment [AB] has been replaced by an arc of a circle which makes a hollow and, on the right, by an arc of a circle which makes a bump.

(« soft diamond » is « losange mou » in French so it is noted Lm)

      The area of Lm 2 is less than that of Lm 1 while the area of Lm 3 is greater than that of Lm 1.

The soft diamonds are the 27 different figures obtained from the traditional diamond by replacing one or more sides with hollow or bumpy circular arcs.

      Above are the 10 soft diamonds that have a larger area than the traditionnal diamond.

      Above are the 10 soft diamonds that have a smaller area than the traditionnal diamond.

      Above the 7 soft diamonds which have an area equal to that of the traditional diamond.

If we take as unit of lenght the lenght of one side of the traditional diamond, the 27 soft diamonds cover a hexagon of side 3 :

      You will notice, in the frame, 18 small pieces of the same color as the frame ; these 18 small pieces allow us to have different arrangements, for example :

I have three pages for you :

•       1) To practice, small shapes : Exercises
  
  
•       2) Shapes using the 27 soft diamonds :Challenges
  
  
•       3) Conjugated shapes : Conjugations

Jacques FERROUL, le 10 janvier 2023
jacques.ferroul[arobase]gmail.com