This game and the knowledge it represents are based on the ancient philosophy that the five Platonic solids are the root of all polyhedral structures existing in our world.

Plato claimed that these five bodies, or solids, represent the five states of matter, also corresponding to the five elements of physical life according to ancient Eastern philosophies:the tetrahedron symbolizes plasma, equivalent to fire;the octahedron gas, equivalent to air or wind;the icosahedron symbolizes liquid, equivalent to water;the hexahedron symbolizes solid, equivalent to earth; and the dodecahedron symbolizes the void (or Bose-Einstein condensate), equivalent to aether (that which is enigmatic beyond words).

Following Plato was Archimedes, who found a new series of polyhedrons known as “the Archimedean solids”.

Leonardo da Vinci studied these solids.and among his studies, his most outstanding polyhedral accomplishment are the illustrations for Luca Pacioli's 1509 book - The Divine Proportion.

Later on Albrecht Durer, (1471-1528),a German painter, made an important contribution to polyhedral literature in his 1525 book, A Painter's Manual. This was one of the first books to teach methods of perspective, and was highly regarded throughout the 16th century. Durer was considered the founder of the net theory, the theory governing the manner by which two dimensional nets fold into three dimensional structures.

A few centuries have passed before the next few major contributions emerged.

Dorothy Maud Wrinch  (1894-1976) was a mathematician and biochemical theorist best known for her attempt to deduce proteinstructure using mathematical principles. She developed a model of protein structure, which she called the "cyclol" based on polyhedral structures. Her research during the 1940s focused on developing techniques for interpreting complex crystal structure x-rays, and mineralogy.

Richard Buckminster (1895– 1983) was an American architect, systems theorist, author, designer, inventor, and futurist. His architectural designs, popularized the widely known geodesic dome baded on icosahedrial structures.   

In 1966, Norman Johnson published a list which included all 92 polyhedral solids known to science at the time (and still considered comprehnsive, and assigned their names and numbers. The polyhedra which are not Platonic, Archimedean, prisms or antiprisms are  thus called the Johnson solids . While he couldn't prove that there were only 92 polyhedral solids, he  conjectured  that there were no others. Victor zalgaler proved in 1969 that Johnson's list was complete.

 In 1971 , Father Magnus J. Wenninger (born  31, 1919) is a mathematician who works on constructing polyhedron models, and wrote the first book on their construction  


© All rights reserved to Tamir Ashman.

(ISR) patent pending No. 221671 (US) patent pending No. 13/975689          

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