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Mathematics

Seven Touching Infinite Cylinders

Ed Pegg

Ed Pegg, Wolfram Research

Posted 10 years ago

In the paper Seven mutually touching infinite cylinders (arxiv), two solutions are given. Here they are in Mathematica. Graphics3D[ Tube[#, 1] & /@ {{{-3.30042,0.,-1.},{22.5284,0.,-1.}}, {{0.,-7.96597,1},{0.,1.82741,1.}}, {{-5.2998,-9.79317,-1.46472},{22.5284,-0.500337,0.936405}}, {{-3.30042,-1.72312,-2.01532},{9.77293,-3.90866,1.6938}}, {{-1.35632,0.443258,3.64979},{12.167,-2.59978,-1.45537}}, {{-3.88208,-7.41485,-0.411606},{11.7311,-0.688465,-2.87777}}, {{-5.46343,-8.8495,-3.22048},{-1.62876,1.82741,2.16067}}}, Boxed->False] Graphics3D[Tube[#,1]&/@{{{-6.49925,0.,-1.},{4.44344,0.,-1.}}, {{0.,-5.56083,1.},{0.,8.75284,1.}}, {{1.28949,13.5583,11.1955},{2.22276,-4.96793,-2.10446}}, {{-4.63263,-0.427663,-4.09331},{1.89964,14.6892,9.66297}}, {{-4.30216,-3.20887,-0.248212},{1.30071,8.30707,4.92139}}, {{0.591434,9.59278,2.94502},{7.87771,-9.28969,-0.806615}}, {{-6.49925,-0.743111,-2.85682},{6.96103,-9.96972,0.83572}}}, Boxed-> False]

In the paper Seven mutually touching infinite cylinders (arxiv), two solutions are given. Here they are in Mathematica.

Graphics3D[
 Tube[#, 1] & /@ {{{-3.30042,0.,-1.},{22.5284,0.,-1.}}, 
    {{0.,-7.96597,1},{0.,1.82741,1.}},  {{-5.2998,-9.79317,-1.46472},{22.5284,-0.500337,0.936405}},
    {{-3.30042,-1.72312,-2.01532},{9.77293,-3.90866,1.6938}}, {{-1.35632,0.443258,3.64979},{12.167,-2.59978,-1.45537}},
    {{-3.88208,-7.41485,-0.411606},{11.7311,-0.688465,-2.87777}}, {{-5.46343,-8.8495,-3.22048},{-1.62876,1.82741,2.16067}}}, 
    Boxed->False]

first tubes solution

Graphics3D[Tube[#,1]&/@{{{-6.49925,0.,-1.},{4.44344,0.,-1.}},  {{0.,-5.56083,1.},{0.,8.75284,1.}},  
  {{1.28949,13.5583,11.1955},{2.22276,-4.96793,-2.10446}},  {{-4.63263,-0.427663,-4.09331},{1.89964,14.6892,9.66297}},
   {{-4.30216,-3.20887,-0.248212},{1.30071,8.30707,4.92139}},  {{0.591434,9.59278,2.94502},{7.87771,-9.28969,-0.806615}},
   {{-6.49925,-0.743111,-2.85682},{6.96103,-9.96972,0.83572}}}, Boxed-> False]

second tubes solution