Morning KB,
Thanks for the confirmation, I believe "Basket-Tube" was a word originally coined by Rocketdyne in patent applications for their method of forming the complex curved walls of their regeneratively-cooled thrust chamber from hydraulically formed nickel-alloy, stacked like a reed basket around a mandrel and brazed together. It seems the word fell out of use after they got the patent I've only seen it in a couple of highly technical books and there are only a few on the web.
I think that's a Rocketdyne LR79, so most likely the Challenge is one fitted to a Douglas PGM-17 Thor ?
Some Thor IRBM's were basin here for a while and they may have had a different designation and of course the Thor formed the basis of the highly successful Delta Space Launcher