Like the Burke 20, the Crosshead is a 20" Andrew Ritchie-pattern folder. Also like the Burke 20, the fold puts both the drivetrain and the handlebars/controls on the outside. (!)

To make the bike easier to manufacture, they use a straight main frame tube which does not allow room for the fold under rear section under it. The rear wheel folds to the side of the frame, increasing the width of the folded package. It appears the only provision for transport once folded is carrying.

Do they say what the frame material is anywhere?

IMO every change they made away from just a straight up 20" Brompton copy - apart from those frame latches - is to the bike's detriment.