The space curve meshing wheel (SCMW) is an innovative gear mechanism based on the space curve meshing theory, and the helix curve meshing wheel (HCMW) is the most common SCMW. In this study, we propose the polyhedral helix curve meshing reducer (HCMR), which is based on the HCMW group. The installation dimension chains of the HCMW pairs are described for different included-angle cases and the HCMW group is produced by combining HCMW pairs. Finally, a polyhedral HCMR is designed with a single input shaft and multiple output shafts, with an adjustable gear box, for which a trial version was produced. The polyhedral HCMR has good application prospects because of its compact structure, high design flexibility, and low cost.