Near-Miss Symmetric Polyhedral Cages

Abstract

Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for P=6 to P=20 with deformation of up to 10%.

Keywords

• uniform polyhedra
• polyhedral cages
• Platonic group
• near-miss cages
• Cayley graph
• protein cage