Scattering functions of Platonic solids

Xin Li, Chwen Yang Shew, Lilin He, Flora Meilleur, Dean A.A. Myles, Emily Liu, Yang Zhang, Gregory S. Smith, Kenneth W. Herwig, Roger Pynn, Wei Ren Chen

Research output: Contribution to journalArticlepeer-review


The single-particle small-angle scattering properties of five Platonic solids, including the tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, are systematically investigated. For each given geometry, the Debye spatial autocorrelation function, pair distance distribution function and intraparticle structure factor (form factor) are calculated and compared with the corresponding scattering function of a spherical reference system. From the theoretical models, the empirical relationship between the dodecahedral and icosahedral structural characteristics and those of the equivalent spheres is found. Moreover, the single-particle scattering properties of icosahedral and spherical shells with identical volume are investigated, and the prospect of using different data analysis approaches to explore their structural differences is presented and discussed.

Original languageEnglish (US)
Pages (from-to)545-557
Number of pages13
JournalJournal of Applied Crystallography
Issue number3
StatePublished - Jun 1 2011
Externally publishedYes


  • Platonic solids
  • small-angle scattering
  • spatial autocorrelation functions

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)

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