A curved staircase including a double helix form with no center support column includes a plurality of stair segments, wherein each of the stair segments is formed from a plurality of rods coupled to a plurality of connecting nodes. The plurality of rods are arranged in a skewed tetrahedral geometry, which causes the plurality of stair segments to form a helical structure when the plurality of stair segments are coupled together. The plurality of rods form a spine on an underside of the plurality of stair segments. A tread is coupled to each of the stair segments. In alternate embodiments, the curved staircase may be formed from sheet metal creased to form a plurality of linear support locations and connecting nodes.