PUZZLE 4- from the 27th October to the 1st November(to be collected by the 2nd November)
A FOOTBALL
A polyhedron with the shape of a football has 32 sides: 20 of them are regular hexagons and 12 are regular pentagons, as you can clearly see in the picture above.
How many vertices and edges does this solid have?
A FOOTBALL
A polyhedron with the shape of a football has 32 sides: 20 of them are regular hexagons and 12 are regular pentagons, as you can clearly see in the picture above.
How many vertices and edges does this solid have?
SOLUTION:
The football has as many vertices as the pentagons have: 12x5=60. As for the number of edges, which are counted twice, there are as many as the edges of all the polygons: (20x6 + 12x5)/2 = 180/2 = 90.
The football has as many vertices as the pentagons have: 12x5=60. As for the number of edges, which are counted twice, there are as many as the edges of all the polygons: (20x6 + 12x5)/2 = 180/2 = 90.
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