We describe two exact geometric constructions of origami spirals obtained by creasing a flat sheet of paper along 2n curves, alternating mountain and valley, where the 2D crease pattern and resulting 3D folding are 2n-fold rotationally symmetric about the center. Both constructions use conical developable surfaces and planar creases. In one construction (conical spirals), the cone patches all share an apex (the center), effectively forming one big (creased) cone. In the second construction, inspired by David Huffman’s “exploded vertex” designs, the cone apices are the vertices of a central regular polygon. Both constructions have planar creases and, in addition to their rotational symmetry, are reflectionally symmetric through the base plane.