Facing Up to Football 2
Now that you know about ‘angle deficits’, you’re in a position to tackle some BIG polyhedra, starting with
the ‘Truncated Icosahedron’…or common football.
All you need to know is that, at each vertex of the football, the manufacturer stitches together 1 Pentagon and 2
Hexagons…and the ‘angle deficit’ takes care of the rest!
And there you are. 32 pieces of leather, and lots of stitching, and you have a ‘truncated’ Icosahedron
(that’s the result of chopping off the corners of an ordinary Icosahedron) that bounces and rolls real well!
But an even better football is the Truncated Icosidodecahedron…so roll up your sleeves, and Tackle This Challenge:
Imagine stitching together a Square, a Hexagon and a Decagon to form each vertex of a large Polyhedron.
Follow the same procedure as last time:
Angle deficits … number of vertices … number of corners of each polygon type … number of actual polygons of each
type.
How many little pieces of leather this time? Not quite double the number needed for the standard football, but nearly!
In fact, the advantage of more faces and more vertices is slightly offset by the fact that the faces aren’t all as
similar as with only the Hexagons and Pentagons.
Which football bounces better? You’ll have to make one of each and try them out…
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