Up and down is authoritarianism and anti-authoritarianism or "I want the government doing more stuff socially" locking people up for identifying as nazis and actual nazi policy are both authoritarian.
Left vs right is the economic side of things. Left is more government intervention in the economy communism is far left for example, while right is less intervention. Slavery being legal is a far right postion but if you go far enough left everyone is a slave to the state.
Constructivism-Essentialism Axis: Identity politics are trash. Pretty much all social inequality can be reduced to the simple fact of class, ignoring things like race, gender, or sexual orientation. It is an inevitable fact that an independently-wealthy person, regardless of their identity, has much less to fear from oppression in the workplace or anywhere else than someone who is poor and vulnerable. Let's say your boss fires you for some reason or another. If you're poor, now you can't pay rent and you're forced to live on the street. If you're rich, hell, you're probably your own boss already and can't be fired, but even if you aren't, you still get to go back to your mansion or waterfront condo and start planning anew. Crime? Theft and substance abuse? Most robberies are because, news flash, people are poor and miserable and jobless and need money to buy drugs to make them less miserable.
Rehabilitative Justice-Punitive Justice Axis: Private prisons are disgusting and create an incentive for special interest groups to try and lobby government to enact stiffer penalties to fill up more corporate gulags with non-violent drug offenders, who are literally some of the most vulnerable, disenfranchised, miserable people in society.
Progressism-Conservatism Axis: We actually aren't moving quick enough to capitalize upon technological and social advances. If we did, we could practically turn this planet into a paradise. Instead, we're stuck squabbling over irrelevancies, or appealing to obsolete and harmful traditions.
Internationalism-Nationalism Axis: There was a time when being left-wing meant you were anti-globalist or alt-globalist. Nowadays, if you say "I'm an anti-globalist", people think you're a fascist or one of those people whining about "all them illegals taking our jobs". Remember in the mid-2000s when it was trendy to hate on sweatshops, the World Bank, the IMF, and pointless wars if you were a lefty? Well, nowadays, it's the populist right who are saying the same exact shit, except they hate sweatshops because they want more protectionism for cozy, high-paying, unionized first-world jobs and not because sweatshops are a crime against human dignity, they dislike the World Bank and the IMF because "da Jews" and not because of their predatory practice of using conditional loans to liberalize third-world countries and make them open to neocolonialist exploitation by multinational corporations, and they want to stop our wasteful military interventions and embrace isolationism not because they give a shit about the lives and livelihoods of the innocent brown people we're constantly bombing, but because "muh tax dollars" could go to something else. Wake up. Corporate power has expanded massively. The rights of workers and indigenous peoples have dwindled to nothing. For fuck's sake, every smartphone has materials in it that literally came from slave labor. What did leftism do in the intervening time? It embraced the bullshit Neoliberal party line about how greed is good, trickle-down works, we need more laissez-faire and not less, and all those people working for pennies an hour in sweatshops should be glad they have jobs at all. Brilliant. What a lovely betrayal of the proletariat.
Communism-Capitalism Axis: Generally speaking, one's quality of life has more to do with the lottery of birth than any natural talents they may have. Most entrepreneurs come from families that were already flush with cash and assets to start with. The idea that everyone has a level playing field to work with is a farce; if capitalism is a 100-meter sprint, then some people get to start at 90 meters. You can't become a millionaire unless you have some sort of asset that you can make use of in the first place. If you already know the path to wealth, if you already have millions invested, then it just keeps snowballing from there. The growth of the return on capital is much bigger than the growth in wages. Wages have stagnated over the past five decades. If you want money, you need to own something you can charge rent on. If you want to own something you can charge rent on, you need money. If you have any hope at all of your descendants becoming wealthy, most of you are going to be trapped as a wage slave for the rest of your life. With the rise of automation and the gig economy, is it really even fair that the rentier class can collect so much wealth and political power from society while leaving nothing for the rest of us? Every corporation is champing at the bit to replace all of us with robots, because they don't want to pay human beings if they don't have to. Class stratification is increasing to the point where democracy will fail and society will fracture into a caste system. Is that really what we want?
Regulationism-Laissez-Faire Axis: Well, we repealed Glass-Steagall, and then the banks formed conglomerates that were too big to fail and had to be propped back up by the government when they predictably shat themselves from taking people's mortgages, packaging them up, and selling them on to other people as though unpaid debts were an asset. Then, they took the bailout money and went right back to doing exactly what they were doing before, with the same risky, over-leveraged investments. Don't people get it? Consumer capitalism is bullshit. You take on huge debts to buy stupid fucking trinkets and shit that belong in the fucking trash, and then you default on it all because debt is cheap and you get paid fucking peanuts for wages. None of this shit would be a problem if people lived responsibly and spent within their means, but if they did, then how could the fucking banker parasites get rich?
Ecology-Productivism Axis: You have to balance both. I'm not an environmentalist for the environment's sake, but for humanity's. We live in an environment. We need to maintain it in order to survive. What's so difficult to comprehend about that? Sustainability is essential, otherwise, civilization will collapse, and all our social advances will regress into a state of barbarism and ignorance.
Revolution-Reformism Axis: How can someone possibly place their faith in gradual reform? All our politicians are bought and paid for by special interests. You can't get a word in edgewise if you don't have money, and the only way to get money in a corporate-bureaucratic-capitalist society is to be a bloodsucking parasite and a dick to your fellow man. Our two-faced politicians pay lip service to populism even as they pull the rug out from under us by eroding the social safety net, reducing taxes for the already-rich, and spending the federal budget on warmongering and pure bullshit. Reformism is just neoliberalism and capitalism dangling the carrot of a living wage, good services and quality infrastructure right out of the public's reach. Spoiler alert: you will never get the carrot.