Stomachion of Archimedes puzzle plan

The Stomachion is one of the oldest puzzles. Stomachion puzzle was mentioned in the Archimedes Palimpsest manuscript written by Archimedes. Among the treatises of the Archimedes Palimpsest is also the stomachion treatise, where this puzzle is described.
 
Stomachion of Archimedes puzzle plan
 

The whole Archimedes Palimpsest is not preserved, but the parts of this manuscript were saved. In the 9th and 10th century Byzantine Empire was the center of European culture and well educated Byzantine people were engaged in preservation of documents, so they made a copy of the Archimedes Palimpsest. Many Byzantine documents were destroyed during the Fourth Crusade, when the Crusaders of Western Europe invaded and conquered the Christian (Eastern Orthodox) city of Constantinople, capital of the Eastern Roman Empire. Shortly afterwards the Archimedes Palimpsest was cut apart, the ink was scraped off, and the parchment was used for writing of prayer book. This prayer book was kept for a long time in the Greek Orthodox Monastery of Mar Saba, and afterwards in the Constantinople library, where Danish philologist Johan Ludvig Heiberg discovered that the prayer book was actually written on the Archimedes Palimpsest

Since only certain parts of this document survived, it is unknown whether Archimedes invented the puzzle, or he just described geometrical aspects of the puzzle. According to the latest researches, Archimedes did not contemplate about Stomachion from the aspect of puzzle (forming some shapes by using the parts), but he examined the puzzle mathematically: in how many ways these 14 pieces could be arranged into a square.     
 
Stomachion puzzle can be also found under the names ostomachion, Loculus Archimedius (Loculus of Archimedes), syntomachion, Archimedes' Box and the 14 piece tangram.

 The original Stomachion consists of 14 pieces that tile a square. Two pairs of pieces are duplicated.
 
Stomachion of Archimedes puzzle plan - Cutting diagram
Stomachion of Archimedes puzzle plan - Cutting diagram

Stomachion is a very interesting dissection puzzle, because it can be solved in two ways:

1. To find as many ways as possible to form a square from the 14 tiles. In November 2003, Bill Cutler found there to be 536 possible distinct arrangements of the pieces into a square, where solutions that are equivalent by rotation and reflection are considered identical. You can see some of the solutions on the picture, and your task is to find as many of them as possible.
 
Stomachion of Archimedes puzzle plan - Square solutions
 
2. To make various geometrical shapes with 14 tiles. Look at the geometrical shapes on the picture and try to form them.
 
Stomachion of Archimedes puzzle plan - Tasks to solve