I believe Odysseus belongs in the category of an epic hero. He shows time and time again how he's a hero, his never-ending determination to get his crew home, his nobility as the king of Ithaca and his part in the Trojan war making him vastly known, battles supernatural foes - Polyphemus for example, he has an almost supernatural strength. The difference I'd put between a classic hero and an epic hero is, a classic hero is unbelievably perfect, not easy to relate to - while an epic hero has flaws, and isn't afraid to show them, while still pushing through.

Odysseus wouldn't fit into the classic hero category for multiple reasons; he isn't unbelievably perfect, showing with how he's got quite a few of his men killed, he also doesn't always follow what's right, showing how despite his crews fear, he let his anger get to the best of him and antagonized Polyphemus, causing Poseidon's wrath, and he also showed he doesn't follow always what's right with how he stayed in Polyphemus' cave, waiting for his return, for an, in my opinion, a sense of greed to see if the cyclops would give anything. The only trait I really realized of an epic hero that Odysseus doesn't hold, is he isn't humble, and can be quite arrogant, letting his anger often get the best of him.

He shows signs of heroism, but I'd say there were times he was a less-than-ideal hero. He shows heroism in blinding Polyphemus to get him and his crew out, he shows heroism in hiding the location of their ship, so Polyphemus didn't destroy it or cease their chances of escape, he shows heroism in taking the sheep's and rams of Polyphemus to have his crew and him have something to eat to survive. But there were times he wasn't very heroic. Such as when he even stayed in Polyphemus' cave in hopes the cyclops would give them something, such as when he antagonized Polyphemus during his and his crews escape, despite his crews fear, due to him being blinded by anger, incurring Poseidon's wrath.

I feel Odysseus is a hero, albeit, he has times where he's not the best, showing how human he truly is, even if there's stories of him. He shows imperfections by staying in Polyphemus' cave out of a sort of greed the cyclops will give something, causing Polyphemus to feast on parts of his crew, he shows imperfections by antagonizing Polyphemus. But he also shows the traits of a hero by making sure who survived of his crew, got out safely, he also took Polyphemus' sheep's and rams to his crew for them to have something to feast on. He's shown imperfections and perfections, showing the truth of a hero can be beautiful and ugly. I'd say he's a hero, and I hope I helped you agree to that.