Related Experiment Video
Updated: Mar 18, 2026

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
Published on: May 8, 2015
Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra
A T Cadotte1, J Dshemuchadse, P F Damasceno
1Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.
Abstract:
We report the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation, it had not previously been observed in self-assembly simulations. Both known one-component phases - the dodecagonal quasicrystal of tetrahedra and the densest-packing of octahedra in the Minkowski lattice - are found to coexist with the binary phase. Apart from an alternative, monoclinic packing of octahedra, no additional crystalline phases were observed.
Related Concept Videos
Structures of Solids
The Seven Crystal Systems: Overview
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Space Trusses
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...
Ionic Crystal Structures
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
Metallic Solids
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....

