A new oxofluoride Co15F2(TeO3)14 has been prepared by optimized hydrothermal synthesis involving a complex mineralization process. The crystal structure consists of a three-dimensional network of CoO5(O,F) octahedra, distorted CoO5 square pyramids, TeO3 trigonal pyramids and grossly distorted TeO3+3 octahedra, which are linked by sharing corners and edges. The Te(iv) lone pairs are accommodated within novel pyritohedron-shaped [(TeO3)14]28- units. This special framework provides a much larger free space that allows Te atoms to vibrate with a large amplitude, which leads to extremely low lattice thermal conductivity. Magnetic susceptibility data for Co15F2(TeO3)14 show antiferromagnetic ordering below 9.6 K with a substantial orbital component to the effective magnetic moment. An S = 3/2 honeycomb-like spin network was carefully analyzed by experimental techniques and first principles calculations.