The correct crown for a Polerouter/Polarouter is specific to the model reference number.
https://universalgenevepolerouter.com/guide-to-locating-model-reference-and-serial-numbers/
All stems are the same thread for most (if not all) Polerouters (and UG perhaps) from this era.
Emily - what is the model reference of your Polerouter?
Timo - a 20360 should have the larger domed style, one that fits over the case tube of the 20360 and is 5.20-5.25mm diameter.
There are some crowns that look very similar on the outside, but are not interchangeable between references due to the internals and different sized case tubes for different references. They will fit the stem of course, but will not fit over the case tube... Ive run into problems a couple of times but have not yet gotten to the bottom of it (the differences are very small).
EDIT: Here are a couple of examples of what I believe to be the correct 20360 reference crown.
They wear down and become more rounded around the edges, but the two here look quite sharp/new:
https://shop.hodinkee.com/products/a-1950s-universal-geneve-polerouter-automatic?variant=31678302468
http://claremontvintage.com/shop/watches/ug_44/
Hope this helps...