Configuration of DNA polyhedra of truncated tetrahedron, cuboctahedron, truncated octahedron

摘要

The synthesis of DNA polyhedra has attracted more interest because of its wide application prospect, but its formation mechanism from mathematical viewpoint remains poorly understood. This paper presents the assembly process and mechanism of DNA truncated tetrahedron, cuboctahedron and truncated octahedron by the means of mathematics and computer program. Firstly, based on the assumption that the total number of all the crossings within each face of a DNA polyhedron must be an even number, potential types for three DNA polyhedra above are calculated by computer programs; Secondly, the projections of the truncated tetrahedron, the cuboctahedron and the truncated octahedron are plotted based on data fetched by the program; Thirdly, the component number, the odd-crossing edge number and even-crossing edge number for the corresponding polyhedral links are computed by analysis of their projections. This study gets some assembly mechanism on the structure of DNA double helix, promoting the comprehending and design efficiency of DNA polyhedra. (C) 2019 Elsevier Ltd. All rights reserved.