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Octahedron in a Cube / Hexahedron

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### #Octahedron in a Cube / Hexahedron

Each polyhedron has a dual or reciprocal, where the faces and the vertices switch to each other. Very few can be easily demonstrated physically by fitting one into the other. The cube seems to be a special case.

A cube (aka hexahedron) is the dual of an octahedron, and vice versa. In this design, we have an octahedron (edge length =42.4mm) that can be slided into a cube (edge length = 60mm). It could be used as a desktop puzzle, especially when using the octahedron halves, or a math model for various purposes.

### #Among the Files

  1. Two versions of the cube box.
  2. A Platonic octahedron
  3. A Platonic octahedron half, two of which make an octahedron.

### #References

  1. http://mathworld.wolfram.com/DualPolyhedron.html
  2. https://en.wikipedia.org/wiki/Platonic_solid
  • 3D model format: STL

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STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

License

CC BY

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