We　report　a　catalyst-free　epitaxial　growth　of　silicon　nanowires　on　polyhedral　facets　of　mother　Si　nanoparticles　by　thermal　evaporation　process.　Single　silicon　nanowires　and　octopuslike　silicon　nanowires　(OSNWs)　were　synthesized　under　different　temperatures.　The　OSNWs　have　several　directions　including　＜　112　＞,　＜　110　＞,　and　the　unusual　directions　of　＜　100　＞　and　＜　111　＞.　A　catalyst-free　temperature-dependent　epitaxial　growth　model　was　suggested.　Using　the　Wulff　theory　and　first　principle　calculations,　these　growth　directions　can　be　explained　by　the　preferential　selection　of　temperature-dependent　surface　energies.　It　thus　revealed　an　important　but　simple　growth　model　in　which　the　growth　directions　could　be　delicately　controlled　through　only　determining　temperature　and　substrate　orientation.　(C)　2008　American　Institute　of　Physics.