Draw a square. Divide it into thirds horizontally. Take the middle rectangle and divide it into thirds vertically, yielding a small square in the center 1/9 the area of the original. Recursively repeat infinitely on this center square. Place electrical resistors on all segments and calculate the resistance between two corners of the original square.
Draw a square. Draw a smaller square inside it. Connect the corresponding vertices of the two squares. Repeat.
Latter is equivalent to a prism with a square grid of resistors on its surface. We can imagine other infinitely long thin geometric shapes: stack of octahedra.