Joe Clinton's Equal Central Angle Conjecture about Goldberg polyhedrons is front page at the moment on bfi.org.

Adrian Rossiter has made some new computer images of a 15 frequency tetrahedral Goldberg and a 20 frequency icosahedral Goldberg. I'm placing them here in the dome section for obvious reasons. Nice work, Adrian and Joe! Next is a mathematical proof. Any volunteers?

Rossiter wrote:
"I made my program more efficient, using a different algorithm, and it turns out that this Goldberg doesn't have a minimum edge length.

Here is one with a shorter edge length (all equal to 10 significant figures) and a good tesselation"

http://www.freewebtown.com/adrian/tmp/tet15e1.gif

"So, all is still well with the conjecture!

Surprisingly, this one has a slight twist. I don't know if
the twist would disappear if I ran the program for longer.

Here are some views of an equal edge spherical Goldberg based on the dual of an F30 tetrahedron."

http://www.freewebtown.com/adrian/tmp/tet15f1.gif

http://www.freewebtown.com/adrian/tmp/tet15f2.gif

http://www.freewebtown.com/adrian/tmp/tet15f3.gif

"This "concentric" tiling appears to be sustainable at higher frequencies, which bodes very well for the conjecture.

I guess I should have a go at an icosahedral one now...Minimal distortion on an F20.

http://www.freewebtown.com/adrian/tmp/ico20g1.gif

All looks good for the conjecture!"

http://www.bfi.org/node/608

Adrian Rossiter
adrian@antiprism.com
Home: http://antiprism.com/adrian