PWrong wrote:[...]

That sounds cool but I completely missed that and I have no idea what's going on there. Which thread should I read first to get an introduction to this idea?

The (15-pages long

) topic "bilbirothawroids" is the split that includes almost all discoveries of CRFebruary. Back then I tried to find these by contracting ids to bilbiros and thawroes, and quickfur was very good at finding them in a seemingly less structured way which gave more interesting polytopes. If you have loads of free time you can read all this, but the most important things are the

first post, which started it all, the discovery of the

J92 rhombochoron (incmat

here), the invention of the

CVP-tool (a tool that gives a measure of the intrinsic complexity of polytopes, it might come in handy some time. The last/recent definition can be found

here), and the discovery of node-changing, which can be found

here, and a summary

here. The other posts of the Bilbirothawroid topic are mostly about individual discoveries, naming schemes and (sometimes very unwieldy) speculations about underlying structures.

The now used process to construct these shapes is by partial expansion. The same partial expansion Klitzing has a

page about on his site, but now with a step in which you change some nodes from x in (-x), with the necessary value-adding. This node-changing if interpreted as things you do to a shape are now mostly seen as taking a faceting of the polytope. The split about this discovey is

"Partial Stott-expansion of nonconvex figures. student5 was the

first to use the process as we use it now. After reading this post, and understanding the node-changing, I guess you will understand what we are doing to make these shapes. In the "Constructing BT-polytopes via partial Stott-expansion"-topic, we have used this to make some very interesting polytopes. I guess Klitzings elaborate

expansion-posts will make the process even clearer. Basically you can do such an expansion on every reflective subsymmetry of a polytope, which is why a big part of this topic is about symmetry groups. Another part is about different definitions of "partial" (real boring, but necessary). Interesting things are from page 4. Introduction at page 1.

Also interesting is D4.11, see the topic "D4.10 and D4.11". It is the first thing which uses a 4-dimensional subsymmetry of ex.

How easily one gives his confidence to persons who know how to give themselves the appearance of more knowledge, when this knowledge has been drawn from a foreign source.

-Stern/Multatuli/Eduard Douwes Dekker