One savours the resulting obfuscation; but blowing your original cube up to a dodacehedron has not improved the (maximal) curvature of the patches! WFL On 3/12/14, Bill Gosper <billgosper@gmail.com> wrote:

Hilarie>

A while back I asked if there was illustration of a project of a dodecahedron to a sphere to a rectangle. Once reasonable way to do the calculation is to compute the vertices on the sphere (a nice collection of 1, phi, and 1/phi for the coordinates), the great circle arcs between the vertices, and to use a Miller projection of that to a rectangle. I've not found a picture of this for a dodecahedron, though. The Internet has pictures of almost every other conceivable representation of a dodecadhedron, just not this one.

A somewhat related question is how would you shrink wrap a ping-pong ball? A rectangle of ordinary kitchen clear plastic wrap stretches nicely across a hemisphere, but the lower part bunches up along longitudinal lines and creates a dense knot at the pole. How would you even describe a solution that minimizes the surface area, short of saying "use a spherical layer of plastic wrap"?

<Hilarie Speaking of such matters, and older ones, here's a three-piece baseball

cover: gosper.org/IMG_0212.JPG , to go along with our one-piece (sphericon) and the usual two. Background: https://www.youtube.com/watch?v=pvT5ySMnO8U

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