Systematic IUPAC name of buckminsterfullerane

Many of you have heard of buckminsterfuller**E**ne, which is C60, also called the "buckyball".


Well, there's also buckminsterfuller**A**ne, which is C60H60. This is a buckyball that's fully saturated (all carbon-carbon bonds are single bonds) and fully hydrogenated.


I'm aware that the nomenclature for polycyclic hydrocarbons can get pretty messy. For non-aromatic hydrocarbons, I've already determined why the systematic IUPAC names (the ones with numbers inside brackets that indicate the "backbones" and bridges) for tetrahedrane, cubane, and dodecahedrane are what they are:


Tetrahedrane: Tricyclo[1.1.0.02,4]butane


Cubane: Pentacyclo[4.2.0.02,5.03,8.04.7]octane


And from the [Hamiltonian path of a regular dodecahedron,](https://commons.wikimedia.org/wiki/File:Hamiltonian_path.svg) I was also able to verify the systematic name for dodecahdrane.


Dodecahedrane: Undecacyclo[9.9.0.02,9.03,7.04,20.05,18.06,16.08,15.010,14.012,19.013,17]icosane


As you can see, with a dodecahedron it starts getting pretty messy, but in the linked image above, if you number the rightmost point as #1, then whichever way you go the point that is connected to #1 via a dashed line would be #11. From then I was able to verify the locations of all the secondary bridges. From my intuition, it seems that you want to number the vertices such that at least one pair of vertices with a bridge has the vertex numbers differing by one-half the total number of vertices.


Now, that got me wondering, what would the same name for a truncated icosahedron be?


I started looking for Hamiltonian paths through a truncated icosahedron, and came across [this paper.](https://core.ac.uk/download/pdf/81935077.pdf) On Page 2, Figure 2, six possible Hamiltonian paths are shown. I numbered the first two of these and found out that the red figure has two bridges where the two vertices' numbers differ by 30 (10/40 and 25/55, the 32/52 in the circle is incorrect). I've numbered them as follows: [![Numbering of vertices in buckminsterfullerane](https://i.stack.imgur.com/XpbcK.png)](https://i.stack.imgur.com/XpbcK.png)


And then after locating the two bridges, I re-numbered the diagram with vertex #1 as one of the vertices in the black rectangle: [![Numbering of vertices in buckminsterfullerane](https://i.stack.imgur.com/K5dWA.png)](https://i.stack.imgur.com/K5dWA.png)


And from there, I tried to deduce the systematic IUPAC name for buckminsterfullerane. This is what I came up with:


**Triacontakaihenacyclo[29.29.0.02,28.03,26.04,23.05,60.06,22.07,58.08,20.09,57.010,18.011,55.012,17.013,53.014,51.015,48.016,46.019,45.021,44.024,43.025,41.027,39.029,37.030,35.032,59.033,56.034,54.036,52.038,50.040,49.042,47]hexacontane**


(man, what a mouthful)


where *triacontahena-* means 31 and *hexaconta-* means 60.


My question is whether this name is correct. And if it's not correct, where are the correct locations for the bridges?


