The only real restrictions on origami are no cutting, and models requiring multiple sheets are expected to have locking mechanisms which make it possible to keep them together without glue (though glue is not forbidden and is encouraged to be used in shaping). Paper doesn't even need to be square, it's just desirable. Curves and twists are completely acceptable, and curved origami is its own niche little area rarely explored due to the difficulty of making a clean curved fold. Jun Mitani is a master of this style.