Soccer ball truncations

Asked Jun 11 '20 at 17:18

Active Jun 11 '20 at 17:26

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A Unit edge Mathematica icosahedron is truncated with hexagon central arc length $ h= 0.3667612 $ that I calculated using spherical trig. How can we take two adjoining points say

aa = {(1 + Sqrt[5])/(2 Sqrt[10 - 2 Sqrt[5]]), 1/2, 
   1/Sqrt[10 - 2 Sqrt[5]]};
bb = {Sqrt[2/(5 - Sqrt[5])], 0, -(1/Sqrt[10 - 2 Sqrt[5]])};
Norm[N[aa - bb]]

and on the circumscribed sphere demarcate the white portions by drawing lines with above $h$ divisions, color the pentagons black and start (mouse) playing with standard soccer ball for fun?

edited Jun 11 '20 at 17:26

asked Jun 11 '20 at 17:18

Narasimham

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Related: 3D graphic of soccer ball. – C. E. Jun 11 '20 at 17:33
FWIW, I don't understand why this question was closed by the Community, and I did not vote to close it. – C. E. Jun 12 '20 at 05:47
https://math.stackexchange.com/questions/3697649/measure-of-an-angle-subtended-by-each-pentagon-in-a-truncated-icosahedron/3715569#3715569 After the above answer I wished to share in the hexagon truncation segment length $h$ for unsophisticated reconstruction of the soccerball in Mathematica. – Narasimham Jun 12 '20 at 06:31

Soccer ball truncations

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