I'n going to input some coordinates with which to build a world based on an initial triangle from the three vertices the user selects.

I can modify this triangle into a pentagon, and the pentagon into a fan of five triangles, and then build out a ring of triangles in a strip more or less around the equator, then another triangle fan around the other pole of the globe.

I have a page which takes three points from me and draws a triangle. When you click again it subdivides the triangle into a pentagon.

Make a tetrahedron from a triangle

Pick three points to make a triangle

Oops!

 They murdered a man on the streets of Minneapolis today. May they rot in hell...

strips of diamonds?

Make rows of triangle strips.

Oops!

Radius

Change to an 'exploded' icosahedron.

Oops!

strip it down

Do something...

Oops!

Something weird, something wonderful.

Spreading out...