TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Paths: The first end of the base member is an inlet and the second end of the base member is an outlet. The first set of paths has first ends disposed at a first interval from the plane, a second set of paths has first ends disposed at a second interval from the plane, and the second interval is different from the first interval, such that the first ends of the second set of paths are offset relative to the first ends of the first set of paths. The base member has an outer periphery and a center, and the second set of paths is disposed closer to the outer periphery than the first set of paths. The first end portions of the paths are arranged to form a ripple shape that extends in a direction parallel with an extending direction of the plane, where a maximum value of the intervals from the plane increases in correspondence with a cell density of the paths. The path at a central portion of the spiral structure formed by the first base member and second base member has the largest interval from the plane. The first end portions of the paths are arranged in a spiral tower shape, and the first ends of the paths are arranged in several steps from a peripheral edge of the spiral structure to the central portion of the spiral structure based on a cross-section of the spiral structure that is parallel to the first direction. Preferred Catalyst Support: The catalyst support is symmetric or asymmetric when rotated about a central axis, the central axis being parallel to the first direction, where the first ends of the paths are tilted from a peripheral edge of the base member to an opposite peripheral edge of the base member based on a cross-section of the base member that is parallel to the plane. The catalyst support further comprises catalyst materials disposed in each of the paths. Preferred Base Member: The base member includes a first base member having a sheet shape and a second base member having a ripple shape and being in contact with one surface of the first base member, the first base member and the second base member overlap and are wound in a spiral structure, and the paths are formed between the first base member and the second base member, sidewalls of the paths being at least partially defined by the ripple shape of the second base member. The first base member and the second base member are formed of a thermally conductive material or a metallic material. The base member is formed of a ceramic material having several penetration holes. Preferred Method: The method (M1) further involves fixing the first base member to the second base member; coating a catalyst material on several paths formed between the first base member and the second base member, where sidewalls of the paths are at least partially defined by the ripple shape of the second base member. Preferred Reformer: In reformer, the target reaction includes at least one of a catalyst-promoted reforming reaction and a catalyst-promoted oxidation reaction. The reformer further comprises a second chamber surrounding the first chamber; and a second catalyst support disposed in the second chamber, where the first chamber has a first spiral structure, and the second chamber has a second spiral structure, the second spiral structure encircling the first spiral structure.