I know that a Truncated Icosahedron is the underlying shape that makes a Football (Soccer ball).

In real life, the 20 Hexagons and 12 Pentagons are cut out of fabric and a balloon inside is blown up in a spherical shape which stretches the fabric giving you a ball shape.

Truncated Icosahedron next to Football

I would like to know if it is possible to create a net for the ball on the right, the hexagons and pentagons that have been stretched out to a sphere. My goal is to be able to cut out 2D shapes and then stick them on a sphere so that it fits together perfectly.

Q1) Is this even possible? Q2) If yes, how do I go about getting the dimensions of the shapes or the net.

  • 2
    $\begingroup$ The spherical ball cannot be made from a net on a flat surface (i.e. a flat piece of card/paper) since the pieces have (positive) intrinsic curvature. Still, it is possible to manufacture curved surfaces, for super accuracy 3d printing might be a possibility. $\endgroup$ – Nick L Feb 20 '18 at 14:03

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