PD Dr. Andreas Paffenholz

The 2s2s Pages

A 2-simple and 2-simplicial 4-polytope is a polytope whose 2-faces are triangles, and we have three triangles around every edge of the polytope.

Until 2003, only a finite number of such polytopes where known. By now, there are infinitely many, they are easy to construct, and we have constructed more than we can put on this page. We present a selection that we render interesting.

On this page is only a short selection. Click on the property title to view a list of all generated and indexed 2s2s polytopes with the given property.

Some additional unsorted polytopes can be accessed here. They all contain their number of vertices in their name. The complete list of all currently available and classified polytopes is here. The directory tree can be accessed here.

The polytopes are all given in the format polymake used until version 2.3. They can be read with newer versions. Most of the files contain geometric data, some only combinatorial. For many polytopes I have also provided files in the jvx format, which is the file format of the geometry software javaview. They can be viewed directly by clicking on "view". (If you have javascript enabled. Otherwise you have to download the viewer from the javaview homepage and the jvx file.)

Some polytopes in higher dimensions with simplicity and simpliciality at least 2 can be found here.

You can downlowd the polytopes descriptions for use in your work. However, I would appreciate an email about any results/ ideas you obtained using them. Here are some references you could cite if you use the polytope descriptions in a paper

Regular Polytopes

2s2s Polytopes from the E-Construction

2s2s Polytopes with Vanishing g2

Part of the polytopes listed below were found by Axel Werner. You can find additional pictures and a polymake client to construct them at his 2s2s page.