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# Katzengold: Pyrite, Plato, and a Polynomial

## General background material

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

Algebra and Number Theory

Didactics and Education

Geometry and Topology

## Connections to other fields

Chemistry and Earth Science

Reflections on Mathematics

## License

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## More general background material

## Mathematical subjects

Algebra and Number Theory

Analysis

Didactics and Education

Discrete Mathematics and Foundations

Geometry and Topology

Numerics and Scientific Computing

Probability Theory and Statistics

## Connections to other fields

Chemistry and Earth Science

Computer Science

Engineering and Technology

Finance

Humanities and Social Sciences

Life Science

Physics

Reflections on Mathematics