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On Sunday, September 17, 2023 at 3:29:21 AM UTC-6, Gerald Kelleher wrote:

 > The balance between pentagonal and hexagonal geometry is not quite
the same thing as a soccer ball which uses a combination of both- 
> 
 > https://media.geeksforgeeks.org/wp-content/uploads/football-157930 960
720.png 

 Of course, the reason that a soccer ball is possible is that the
(pentagonal) dodecahedron
is the dual of the icosahedron.

 Hence, the truncated icosahedron leaves pentagons at the icosahedron`s
vertices when
they`re trimmed to turn the triangles into hexagons.

John Savard
--- G2/1.0
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