To be fair, the character of Box was vastly dumbed-down from the book's description. The book version of Box is a menacing cyborg figure with a half-flesh, half-metal face and a cutting tool for a hand. He's one of the inhabitants of Hell, an escape-proof prison colony in the far North, of which the ice caverns of the movie are just a dim reflection.
The book's authors actually wrote a screenplay that sticks close to the book as written. I'm sure it would've made a much better movie. If Logan's Run ever gets rebooted, I hope they dig out that old script and use it.