A ring of 10 acute golden rhombohedra (AGR) is used as a backbone for building a ring of 10 rhombic hexecontahedra (RH). The idea is based on the fact that 20 AGR produce an RH, and an AGR is composed of an octahedral part and two tetrahedral parts. Although previous Demonstrations dealt with this subject, this approach gives a better and more detailed understanding of the possible structures that can be found within the ring of 10 RH.