# World Tour of Planet Rhombicosidodecahedria

This is the planet Rhombicosidodecahedria:

This lovely planet has 62 countries, each with its own distinct history and culture. By an amazing coincidence, the countries all happen to coincide perfectly with the faces of a rhombicosidodecahedron. You, as a tourist, are naturally hoping to visit all of them.

How many different ways can you travel though each of the countries on this planet, visiting each exactly once?

Some rules:

• Your tour may start in any country you wish.
• You must visit each country exactly once. Once you have visited a country, you cannot visit it again. (The word "tour" should not be taken to imply a requirement that you return to your starting point.)
• You may only move between countries that are adjacent. In other words, each new country you visit must share a border with the previous one. (If they just touch at the corners that doesn't count.)
• For purposes of this puzzle, every country should be treated as unique, and reflections and rotations all count as different paths. (In other words, the orange pentagon counts as a different starting point from the purple pentagon.)
• matrix mapping part is harder than writing a code to find all possibilities :D
– Oray
Mar 11 at 7:47
• @Oray - rot13(V ubcr lbh qvqa'g jvaq hc fcraqvat gbb zhpu gvzr gelvat gb oehgr sbepr guvf. Vs lbh qvq, V ncbybtvmr. Guvf vf qrsvavgryl bar bs gubfr chmmyrf jurer oehgr sbepvat vf qbvat vg gur uneq jnl! V jnf grzcgrq gb tvir guvf gur "ab pbzchgref" gnt, ohg V jnf nsenvq gur zrer cerfrapr bs gung gnt jbhyq tvir njnl gur frperg.) Mar 11 at 19:44
• haha don’t worry i did not :)
– Oray
Mar 12 at 7:18
• In graph theory (but also in common parlance), the word "tour" implies returning to your starting point. Is this your intention? It seems to contradict the requirement of not visiting any country twice. Mar 21 at 0:29
• @Oliphaunt - I edited the rules to clarify this a bit. Mar 21 at 17:17