I am trying to texture a sphere made up entirely of equal size triangles (varying numbers of triangles at different levels of detail).

What is the best way to texture it (basically which map projection)? Basically, I want the texture spread as evenly as possible, with as little distortion as possible (especially when the number of triangles is low).

This is my leading candidate. But I would like to know if anyone has a better suggestion.
http://en.wikipedia.org/wiki/Peirce_quincuncial_projection

Anyone do this before and/or have any tips?

There are no perfect answers.

A simple technique is like the skybox - a cube of 6 square textures that get radially projected down onto the sphere.

Equal area projections can be good to ensure "pixels of texture per unit area of sphere" is constant. But there can be unfavourable stretching in one direction and squashing in another direction.

Equidistant projections kind of do something opposite, and ensure there is no local stretching and squashing, but don't guarantee pixels:area constancy.

One projection is both equal area and is equidistant (but in a restricted way): Lambert azimuthal equal-area projection. You may find this works well

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I prestreched the texutre last time I did this. I used Lightwave to do it IIRC, morphing a tex mapped sphere into a flat plane and grabbing the result as my new texture.

I can't remember exact details as it was a long time ago.

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10 PRINT "Bad Monkey ";
20 GOTO 10