Is there, or has there ever been, an unambiguous word for "the leftmost extreme" or "the rightmost extreme"? Such words exist for the other two dimensions.
Imagine you are floating in a cube in space.
Probably not, because left and right are often more vague compared to the other "limits". If you're approaching e.g. a round hill, "top" means the hill's summit, "bottom" generally means the lowest point of the hill that's closest to you. Left and right "limits" don't really mean anything, since you can go around the hill. Same applies to a sphere like the Earth etc. Some objects may have defined left/right "ends" but the word used then is usually specific to the shape. If it's a sheet of paper, the word would be "edge". If it's a building and you're on the ground, the word would be "corner" etc. If you're facing separate objects, like a row of columns, you can say "the leftmost/rightmost column".
If you assume that you are confined in a cube or cuboidal walled room or enclosure looking straight ahead or floating in a spaceship...
You can go up until you hit the top structure or roof.
You can go down until you hit the bottom structure or floor.
You can go forward until you hit the front wall.
You can go backward until you hit the (back/rear) wall.
You can go left until you hit the left wall.
You can go right until you hit the right wall.
These are 3 dimensions or 6 axes if sense of movement vector is considered.
There's no single word for these, we would just say "left face" or "right face".
If, instead of a solid like a cube, we were talking about something more linear (like a line, or a road on a map), you could say "beginning" for the left extreme and "end" for the right extreme. Absent other context, we tend to consider progression from left to right (west to east on maps), similar to reading. But note that this would change if the direction of motion along the line is known; then "beginning" is wherever you started, and "end" is the destination.
Imagine you are floating in a cube in space.
Port and starboard work well with marine vessels and aircraft who often deal with such orientation issues.
I presume space personnel use similar terms to aircraft folks.
Port and starboard unambiguously refer to the left and right side of the vessel, not the observer.
Why is port-starboard terminology used in aviation?.
port/starboard, fore/aft, top/below
"You can go (left) until you hit the cube's portside."
'Left' and 'right' in the political sense are are relative to each other. The distinction was first drawn in the French revolution. In the French assemblé, supporters of the king sat on his right, while opposition to the king sat on his left. Clearly the distance they sat to his left or his right was not necessarily a measure of the strength (or extremity) of support or opposition.
Left and Right in more recent times have to do with aspects of a politician's or a party's economic and social position or policies. It has nothing to do with the whether or not a nation should reject or acquire a monarch or junta. But the politics around the world are a bit like the world as we now know it: spherical rather than flat. So the left and right can meet at their respective extremes in Soviet communism and military dictatorship in both of which the mass population find themselves poor and powerless, ruled by a dominant ruling caste, monarchic, religious or military.
The common way of dealing with the 'wings' of politics is the use of the word 'Far' as in 'far' (or sometimes 'extreme') left and right.
In math, the extremes of the left-right axis are called -∞ and +∞ .
