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Katzengold: Pyrite, Plato, and a Polynomial
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Katzengold: Pyrite, Plato, and a Polynomial
What are the similarities of the mineral pyrite, the dodecahedron as the fifth Platonic solid, and a polynomial of degree 16? This paper explores this connection by using the free software SURFER of the IMAGINARY open mathematics platform, which leads to fascinating pictures displaying transformations from a cube to a dodecahedron, to a rhombic dodecahedron, and to an octahedron, using a single formula. A survey on the ideas and the mathematics behind these visualizations is given. In fact, everyone can explore and modify these forms in real time using the SURFER software. Moreover, the authors have created a short movie, demonstrating the simple geometric beauty.
Mathematical subjects
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Algebra and Number Theory
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Didactics and Education
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Geometry and Topology
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Chemistry and Earth Science
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Reflections on Mathematics
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Mathematical subjects
![](https://www.imaginary.org/sites/default/files/styles/icon_320px/public/algebra-12.png?itok=WMnSOls0)
Algebra and Number Theory
![](https://www.imaginary.org/sites/default/files/styles/icon_320px/public/analysis-06.png?itok=O4i7d5Wv)
Analysis
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Didactics and Education
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Discrete Mathematics and Foundations
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Geometry and Topology
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Numerics and Scientific Computing
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Probability Theory and Statistics
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Chemistry and Earth Science
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Physics
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Reflections on Mathematics