What's an alternative way to classify or describe governments?

I've been trying to find a way to classify governments that isn't right or left. That distinction is already arbitrary in real life and too simplistic for modern scenarios, and just useless for a world that never had the French Revolution (because there's no France, or any Earth countries or landmasses). The best alternative I can think of would be the [political triangle](https://preview.redd.it/a14tp1fwbbq01.png?width=1080&crop=smart&auto=webp&s=0ee257dd1c398c18eae1d3cc80224f6484537ec3). That's just one of many variations. I don't want to use the standard left-right spectrum because I don't think it maps well onto my cultures that are inspired by pre classical/ancient societies rather than medieval or modern ones. I had also heard of a system that groups rulers or ruling classes into 4 types: priest (religious), warrior (military), merchant (trade) and beureaucrat (tests, layers, paperwork, etc).

Have you made anything specific to your world?