How big is this tower?

@TCAT117 Ideally big enough for the empire's leading academia to be located there, if this is not possible, how big is possible?

"big enough for the empire's leading academia" naturally, that depends on how many people that is. And their books, laboratories, etc, etc.

@RonJohn that advice is best put under almost any question here. Star trek, star wars, whatever makes money - they don't care and excessive focusing on details to make it boring for the reader, well, see the meta post if anything made it into published work yet. However for once I think the question does stand without it because it asks if a common idea is possible taken literally. I don't want a discussion, I hope it is ok to let both comments just stand side by side so it is clear that this is not everyone's view.

Time setting could matter significantly. Lab grown ivory is actually close to becoming a real thing. This seems better than mass slaughter as a way of demonstrating academic dominance. As an added plus, ivory could be grown in shapes and sizes not found in nature, which could simplify construction.

This looks like a good source for answering how ivory would behave as a building material.

@RonJohn I disagree: if the nature of its material is an important aspect of the world or story — maybe the tower is vulnerable to certain weapons, — then things like this would be important. We accept that Superman is vulnerable to kryptonite because, though we know nothing workable about how he actually gets his powers, it makes sense that something equally unknown but from his home planet would have something to do with reducing said powers: it has an internal consistency. Ivory is something which we know about from our world.

There is a bigger question, though: where is its companion ebony tower?

One thing to consider is that wood is good for building things from not only because of its material properties, but also the size and shapes that it grows in. I can imagine that ivory probably has decent properties for building; but curved pieces less than 1m long are going to be far from ideal for making structures.

Would vegetable ivory be acceptable? That can be farmed to match the sustained demand of construction. You could farm it on plantations on a remote island with restricted access, ban trade on it, and make using it an imperial privilege.

Depending on how fantastical your setting, you could of course invent a creature that can perpetually regrow its tusks if they're removed.

@RonJohn - That depends on the setting - in a fantasy-myth-and-magic setting like Star Wars, you're correct. However if you're going for a realistic setting and you're trying to portray, for example, a megalomaniacal character who emphasises his power by having a tower made of ivory despite the difficulty (and cruelty to elephants?) in making one in reality, then it doesn't make sense to just say "oh in this world we can make towers from ivory". The use of the "reality-check" tag would suggest the OP is going for this. One wouldn't use it in a question about "The Force" in Star Wars.

IIRC The Neverending Story features one... so.. it's been done before.

I just want to point out that I believe the original reference to a academics studying in an ivory tower refers to an ivory-colored tower, implying it could be actually constructed from any milky-white stone such as marble or simply painted with ivory paint. I'll try to find a source.

Something that might interest people; having visited Alaska where they do gold excavation. They use front end loaders to load the sleuths. Anyways I was surprised to find a collection of large curving tusks piled beside their trailers. When I asked what they were I was told they were Mammoth and Mastodon tusks. I examined a small piece that had broken off, and when said that this was amazing, the amused owner told me to take it home. Then going into the shops there are ivory figures, chess pieces all legal because it isn't from elephants. But it is still ivory. Apparently there is a lot of it.

@can-ned_food The companion tower is the the city of Wonder, constructed by Emperor Steve. He was the staunchest ally of the McCartneyites, builders of the Ivory tower

@Quaternion Same thing in Siberia. That might actually be the perfect source of ivory for a one time building project.

Have you considered grinding the ivory down and making bricks out of it with a polymer? Since it's really dentin that we're talking about here, and that's found in almost all teeth, you'd increase your sources for it far beyond elephants, walruses, etc. You could even become a real tooth fairy, paying kids for their baby teeth!

Are you aware an "ivory tower" is a negative thing ??

@Fattie depends on context. "Your neck is as beautiful as an ivory tower" doesn't sound that negative. Also you could just slap on a coat of paint on any tower and it would literally be an ivory tower, since 'ivory' also means the colour. I don't know enough Hebrew to say whether the original verse meant the material or colour.

@PeteKirkham That is such an interesting question I figured I'd ask it.

Man, the phrase "ivory tower" or "you live in an Ivory tower" is an absolutely established idiom in current English. It is a negative thing. Entirely and totally. There is no "context". It has one fixed meaning. It means a person is "impractical". That's it.

I'm not sure why you mention Hebrew. It's simply from the equivalent French phrase. I believe it was originated by the French writer St.-Beuve. (Note that, I do not know or care about the origin. The phrase is a completely standard idiom in English. It is a pejorative and it means "impractical" - "uncaring". You might apply it to say a member of the royalty, or a scientist.)

Won't somebody please think of the elephants?