We present what is to our knowledge the first observation of spin-polarized atoms cooled within a reflecting cylinder in a high-power medium. A low-pressure vapor of cesium atoms is stored in a glass cell whose volume is 58 cm(3). Cooling laser light (lambda=852 nm) is injected into the cell by optical fibers and is recycled by multiple reflections from the walls of the cylinder. The technique used in this experiment greatly simplifies the generation of laser-cooled atoms. A maximum of 2.5 x 10(8) cold atoms was detected by a time-of-flight technique. The damping of atomic motion has lead to temperatures as low as 3.5muK .