The Platonic and Archimedean solids are uniquely interrelated as a result of


commonly shared symmetry elements; juxtapositioning of faces, vertices, and edges;


and volumetric similarities.  As a result they are inter-transformable via inscription,


compounding, truncation, and sectioning and rearrangement.  And they can be


packed together in a variety of combinations to fill space while maintaining a strict


ratio of tetrahedral to octahedral equivalent volumes.  Thus the ordering principles

inherent to the structure of space offers different forms the potential to transform
themselves into a myriad of diverse shapes while maintaining uniformity in the
     In the following lesson you will see how these abstract geometric properties find

their real life embodiment in the way that the atoms of elements and minerals pack

together structurally.  This in turn determines their physical and chemical properties.

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page 23 of lesson.

Page 22    Geometry rules! - Conclusion


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