Small transmitting aka "magnetic" loop antennas are often constructed out of copper or aluminum pipe material. Antennas don't need to be solid due to the skin effect. Does the skin effect take place on both surfaces of a pipe conductor, outside and inside, or only the outside? (I don't understand the underlying physics)

Where I am going with this is: if instead of a pipe, I use a broad sheet metal piece which is to have the same "active surface" area that corresponds to a wouldbe pipe that a magloop calculator spat out as efficient enough: It does not have an inside - it's solid, though thin. I guess given that it is thicker than a few skin depths at a given frequency, do both sides of the sheet "count" as active surface for the RF current in a resonant loop, and if the inside surfaces, OTOH, of a pipe do not contribute, would that mean that a sheet metal piece with, let's call it "top", surface equals that of the outer surface of a half pipe, and the "bottom" surface of the sheet likewise equals the other half pipe's outer surface, one could get away with half the material when using the sheet metal vs. the pipe, yielding the same efficiency?

-- EDIT: sketch of the question: Left are a loop of pipe material and its crossection below, right are a loop of sheet material with its crossection below.

EDIT: Example of a small transmitting loop. My question regards the outer loop. The smaller one inside is a coupling loop where the RF is fed, and not very visible, at the top gap, a variable capacitor for tuning the resonance frequency.