Changing nodes on CD-diagrams from negative to positive is an interesting process, and has shown to be very helpful at discovering new polytopes via Stott-expansion. Here I'll try to explain how node-changing works, why it works and how it can be used to calculate coordinates. (I guess Wendy finds this interesting)

How node-changing works:

Node-changing works on any diagram. Let's say we have a diagram x5u3o4q, then you can change any node from positive to negative according to the following rules, and you are guaranteed to get the same vertex-set.

1. You can only change a node from A to -A (A is allowed to be negative at the beginning)

2. when you change a node from A to -A, all other nodes must change accordingly. When you have a node B and the branch between A and B has value n (n can be a rational), B gets the value B+2Asin(90-180/n), or B+Astr(n) when str() takes the shortchord of a xno-polygon.

So when you change x to (-x), you get (-x)5(u+f)3o4q. When you change u to (-u), you get (x+uf)5(-u)3u4q. You can do iterative node-changing, so when you have (x+uf)5(-u)3u4q, you can change e.g. the u to -u, and you get (x+uf)5(-u+u)3(-u)4(q+uq) = (x+uf)5o3(-u)4(3q). Of course you can do this more times. in the given example, you can do this infinitely many times.

Why node-changing works:

You might know that the construction that makes a square from x4o starts with two mirrors with an angle of 180/4=45 degrees (or pi/4 radians). what you do next is place a vertex at a distance x of one mirror and a distance o of the other mirror. Then you keep reflecting in the mirrors until you have a square. In total this gives you four vertices: the original vertex, a vertex after reflection in the x4.-mirror, a vertex after reflection of the former vertex in the .4o-mirror, and a vertex after reflection of the former vertex in the x4.-mirror. . So you have four vertices. what node-changing does is that you take a different vertex than the original vertex as seed-point, and then the construction gives the same vertex set. (That the vertex was given by the Wythoff-construction means it gives the same vertex-set, because the vertices more or less form a group). So when you take x4o, you can change this in (-x)4q. Changing q in (-q) gives you (-x+qq)4(-q)=(-x+u)4(-q)=x4(-q). A further changing of x in (-x) gives you (-x)4(-q+q)=(-x)4o. . Changing node A in -A means you reflect the seed-point in the mirror of A.

So in short node-changing ables you to start the kaleidoscope-construction with any vertex of the polytope.

How node-changing can help finding coordinates:

The value of a node on a diagram gives the distance of the vertex to the corresponding mirror. This means the vertex lies on a (hyper)plane parallel to the mirror with corresponding distance to it. Every node gives a new hyperplane on which the vertex must lie, and thus the vertex must lie on the intersection of these hyperplanes. When you have all such hyperplanes, you have located a point. this means the decorated CD-diagram can be seen as a coordinate for a point in a special coordinate-system. The node-changing rules now give you tools to locate aal vertices of the polytope in the alternate coordinate system. I guess these node-changing rules aren't that hard to implement in a computer, and thus you can quite easilly find coordinates from the decorated CD-diagram. The "normal" coordinate system is given by the 222-symmetry. the only thing you need now is a transition from the alternate coordinate system to the 222-system. This can be done, and thus you can easilly obtain coordinates with the new node-changing devise.

so any Coxeter-group can be given a coordinate-system, and that can be used to find a polytopes' coordinates.

Taken into account that values on nodes haven't been published before, I think the new coordinate-system thing, together with the node-changing and the values-on nodes in general are sufficient for a small independent article in prefix of the article about pSe's. We might very well submit the two articles to the same paper to be published simultaneously as two independent but connected articles.