Cube Dissection by Elusive Cube: 176 Magnets, 14 Crystall Lattice Structures

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SUMMARY

The discussion centers on a cube dissection project by Elusive Cube, utilizing 176 magnets that allow for versatile connections without repulsion. The creator demonstrates the ability to construct all 14 crystall lattice structures, starting from an irregular tetrahedron to a rhombic dodecahedron. The project emphasizes the principle of achieving maximum structural diversity with minimal identical volume blocks, and hints at a forthcoming demonstration related to Hilbert's third problem, which remains partially unresolved according to Marjorie Senechal's article published by Smith College.

PREREQUISITES
  • Understanding of crystall lattice structures
  • Familiarity with magnet-based construction techniques
  • Knowledge of geometric solids, particularly tetrahedrons and dodecahedrons
  • Awareness of Hilbert's third problem in mathematics
NEXT STEPS
  • Research the properties and applications of crystall lattice structures
  • Explore advanced magnet construction techniques for geometric modeling
  • Study Hilbert's third problem and its implications in geometry
  • Review Marjorie Senechal's work on tetrahedrons and space-filling problems
USEFUL FOR

This discussion is beneficial for mathematicians, geometric modelers, educators in mathematics, and hobbyists interested in advanced construction techniques using magnets.

minima
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Hi,

I have made a cube dissection, please check my short videos

www.youtube.com/elusivecube

I use 176 magnets that never repel so there is a absolute freedom in connections,
By far the best attributes are that I can build a whole concentric hierarchy of solids
starting with a irregular tetrahedron and ending up with the rhombic dodeca hedron.

I can build the 7 basic crystall latice structures, well actually all 14 are possible.
Have this set for about a decade and still discovering new structuresw all space fillers, all at the lovest common denominator. "Do more with less"

All the build solids are build by the least number of volume identical blocks, in a very near future I will demonstrate Hilbert's third problem.

Smiths College published a article by Marjorie Senechal 'Which tetrahedrons fill space" according to the article this problem is stil not completely solved, but I believe I do have the solution, so please watch my next realese.

Thank you
frank
 
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