Polyhedral nano- and microstructures with shapes of faceted needles, rods, rings, barrels, and double-tipped pyramids, which we call graphite polyhedral crystals (GPCs), have been discovered. They were found in pores of glassy carbon. They have nanotube cores and graphite faces, and they can exhibit unusual sevenfold, ninefold, or more complex axial symmetry. Although some are giant radially extended nanotubes, Raman spectroscopy and transmission electron microscopy suggest GPCs have a degree of perfection higher than in multiwall nanotubes of similar size. The crystals are up to 1 micrometer in cross section and 5 micrometers in length, and they can probably be grown in much larger sizes. Preliminary results suggest a high electrical conductivity, strength, and chemical stability of GPC.