Conclusion |
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The Platonic and Archimedean solids are uniquely interrelated as a result of |
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commonly shared symmetry elements; juxtapositioning of faces, vertices, and edges; |
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and volumetric similarities. As a result they are inter-transformable via inscription, |
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compounding, truncation, and sectioning and rearrangement. And they can be |
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packed together in a variety of combinations to fill space while maintaining a strict |
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ratio of tetrahedral to octahedral equivalent volumes. Thus the ordering principles |
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| 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 | |||
| aggregate. | |||
| 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 |
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| together structurally. This in turn determines their physical and chemical properties. | |||
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Page 22 Geometry rules! - Conclusion |
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