Welcome Mecejide!
At least I finally get what you are after, when speaking of a "quarter(ß5o5/2o5ß)":
x5o5/2o5x happens to be a double cover of
sophi.
ß5o5/2o5ß then is the holosnub of that wrt. vertex alternation.
Thus when starting only with sophi itself and applying vertex alternation (in a holosnubbed manner) thereon, you would be kind of speaking of "half(ß5o5/2o5ß)".
But it happens that this alternation would result in doubled up elements in turn, that is, you could consider to reduce these once more - and this is, where your "quarter" derives from.
But you should be aware that the mere holosnubbing aka vertex alternation of a unit-edged sophi would produce pentagrams of side length f=1.618 both as faces for sissid (= holsnubbed gad) and stap (= holosnubbed pip), and of isosceles triangles with base f and lacing sides q=1.414 for those stap triangles.
When you now proclaim that the result ought be a new
uniform polychoron, then you assume that both types of edges should be
simultanuously resizable back to unit length. The existance of the alternating surely is the trivial part. That one always exists as desired. Just apply the construction device. But the possibility for such a simultanuous resizement surely is the non-trivial part. And in fact I don't see for now, whether that one will be possible or not. You surely should point out an according clue, if you'd feel that it will be possible.
--- rk