# Minimizing the Ratio ofMaximum to MinimumDistance in 3 Dimensions

The following pictures show n points in space so that the ratio r of maximum distance (shown in red) to minimum distance (shown in blue) is the smallest known.
 4. r2 = 1Trivial.(regular tetrahedron) 5. r2 = 12/7 = 1.714+Found by David Cantrellin March 2009.(3-fold rotational symmetry) 6. r2 = 2Found by David Cantrellin March 2009.(regular octahedron)

 7. r2 = 2.293+Found by David Cantrellin March 2009.(3-fold rotational symmetry) 8. r2 = 1 + √2 = 2.414+Found by David Cantrellin March 2009.(square antiprism) 9. r2 = (9 + √129) / 8 = 2.544+Found by David Cantrellin March 2009.(3-fold rotational symmetry)

 10. r2 = 3.101+Found by David Cantrellin March 2009.(4-fold rotational symmetry) 11. r2 = 3.384+Found by David Cantrellin March 2009.(3-fold rotational symmetry) 12. r2 = (5 + √5)/2 = 3.618+Found by David Cantrellin March 2009.(regular icosahedron)

 13. r2 = 3.947+Found by David Cantrellin March 2009.(asymmetric) 14. r2 = 4.168+Found by David Cantrellin March 2009.(asymmetric) 15. r2 = 4.398+Found by David Cantrellin March 2009.

 16. r2 = 4.553+Found by David Cantrellin March 2009.(2-fold rotational symmetry) 17. r2 = 4.771+Found by David Cantrellin March 2009.(5-fold rotational symmetry) 18. r2 = 5.047+Found by David Cantrellin March 2009.(5-fold rotational symmetry)

 19. r2 = 5.409+Found by David Cantrellin March 2009.(4-fold rotational symmetry) 20. r2 = 5.799+Found by David Cantrellin March 2009.(asymmetric) 21. r2 = 5.985+Found by David Cantrellin March 2009.(2-fold rotational symmetry)

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