assigned by administrator Random 2-Sphere RandomSphere Michael Joswig TU Berlin
Strasse des 17. Juni 136 10623 Berlin Germany
joswig@math.tu-berlin.de http://www.math.tu-berlin.de/~joswig Konrad Polthier TU Berlin
Strasse des 17. Juni 136 10623 Berlin Germany
polthier@math.tu-berlin.de http://www-sfb288.math.tu-berlin.de/~konrad Triangulated 2-Sphere on 200 vertices.

This is a very interesting example, because it was not known before that spheres can have as many as 200 vertices. Spheres can be computed with computers.

Here is a table in blockquote max xd
0 <= x1 <= 1
e x1 <= x2<= 1 - e x1
e xk - e g xk-1 <= xk+1 <= 1 - e xk + e g xk-1 , where 2 <= k < d.

Explanation of some words.

Sphere
A round geometry with unique center.
Vertex
A round point on a sphere.
These formulas are useless in the current context: H2O and E = mc2.

52B11 53Axx 53Bxx random polytope nice manifold sphere triangulation 665.00012 polymake 1.3.1 Erwin C. Grabowski Spherical Blow-Up Experimental Mathematics 1--99 1999 3 1 Erwin C. Grabowski Numerics of Sphere Blow-Up TU Berlin 1999 Erwin C. Grabowski Spherical Blow-Up Numerics of Sphere Blow-Up Karl Edit TU Berlin 1999 1--99 Erwin C. Grabowski Spherical Blow-Up 1999 Preprint Erwin C. Grabowski Home Page http://www.homepage.org/ RandomSphere_Master.obj 6377 RandomSphere_Preview.gif 6377 240 240 RandomSphere_Applet.obj 6377 r3-200.obj 6377 RandomSphere_Original.poly 6377 240x240 preview