perplexus.info :: Shapes : Odd soccer ball

Odd soccer ball (Posted on 2003-12-04)

A common 6-in.-radius soccer ball contains 12 pentagons arranged so that every pentagon is separated from the next by the same arc length as one of the spherical (great circle segment) sides of the regular hexagons. As the hexagons are regular, this is the same arc length as one of the sides of the pentagons, as the pentagons also border the hexagons.

Calculate the arc length of a pentagon's side of a new soccer ball using the same radius and instead of one line of separation between pentagons, use two lines of separation between pentagons and consider every new line with a distance equal to a side of a pentagon. (See picture)

Note: The endpoints of the mentioned lines intersect with the surface of the soccer ball or sphere.

Submitted by Antonio

Rating: 3.5000 (4 votes)

Solution: (Hide)

Solution: Find an equation that relates the separation between pentagons including the two mentioned distances that are inscribed touching the vertex of two pentagons, solve for the variable of the resulting transcient equation.
Answer: The spherical sides of every pentagon would be 1.78880986455in.
(See comments for more details)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2023-07-17 09:41:20
re(2): solution	SilverKnight	2003-12-04 17:53:38
re: solution	SilverKnight	2003-12-04 16:49:07
solution	Charlie	2003-12-04 16:31:53
Solution	Penny	2003-12-04 16:25:37

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