In an answer, I suggested the use of "whose" as the possessive of "which." I had a momentary twinge of doubt about its correctness, quickly checked the American Heritage Dictionary which gives "2. The possessive form of <em>which</em>." as the second definition, but find from further Googling that it's may be more controversial than I thought. oxforddictionaries.com does not list "possessive form of <em>which</em>" as a definition so this might be a US/British thing.
I can say that this usage comes <em>very</em> naturally to me, and that it is <em>very</em> common in technical writing.
I'm going to give some actual quotations. What do you think of these sentences? Do they feel correct to you, or do you find them jarring? If you find them jarring, how would you rewrite them? Can you cite any really authoritative source that speaks to this question?
1. Figure 17 shows a contour map of the function F for a cathode whose length is ten times its diameter.
2. In the first step, the satellite is launched into an elliptical transfer orbit whose apogee is at the distance of the final orbit.
3. Unlike the Moruya Suite, this does not extend to very felsic compositions, with a maximum SiO2 of 67-15%, in a rock whose composition is thought to be close to the primary melt composition (Chappell 1984; Burnham 1992).
4. A regular polyhedron is a polyhedron whose faces are congruent regular polygons and whose polyhedral angles are congruent.
I don't find them jarring at all and probably wouldn't think twice about them. You could write "a cathode, the length of which is ten times its diameter." Likewise you could write "the apogee of which,""the composition of which," and "the faces of which." I'd have to do some searching to see if there's a hard and fast rule, though.
It does feel a bit awkward to use "whose" for non-human objects (e.g. it feels 'off' in "I'll buy the car whose seats are leather"), but it's often less awkward than all the other choices. I could easily rewrite the sentence above as "I'll buy the car which has the leather seats", but sometimes it's not so easy to rewrite a sentence like this. When it's a toss-up between "whose" and something like "of whom", I'll usually go with the former.
For things, "noun + of which" sounds more formal than "whose + noun"
However, your sentences all sound normal to me. I am not aware of any variation of usage between the UK and the US on this issue.
I will be following these discussion closely because I always struggle with the use of WHOSE and WHOM (I am an English learner!)