Two-point resistances of symmetric polyhedral networks

Two-point resistances in symmetric bracelet resistor networks: accurate estimates and exact expressions

“…The example of the n-bracelet remains particularly rich to illustrate the different ways that a physicist takes while looking at a given problem, including an initial qualitative assessment of symmetries, the use of elementary methods whenever they yield a quantitative result without effort, and the application of more sophisticated systematic methods [8][9][10][11][12][13][14][15][16][17]. RNs, essential tools in many applications [1][2][3], are also emerging as generic systems in which the various aspects of the physical approach can be learned, practised and constantly improved in efficiency and subtlety to better understand the ways of nature.…”

“…In parallel with these achievements, physicists returned to neglected basic networks. Exact expressions of the equivalent resistance between two nodes, called two-point resistance (TPR), have been obtained for symmetric networks constructed using Platonic, Archimedean or Catalan solids, using elementary methods [7,16] or creative computational methods [17]. Due to the growing number of theoretical results and practical applications in science and technology, RNs and the various methods used to study their properties need to be introduced to physics students.…”