Supplementary Information

Packing Details

The coordinates of the vertices of the 72 tetrahedra in the fundamental cell of the densest known packing are as follows: TetrahPack.72.txt.

The fundamental packing characteristics of the optimal lattice packings of the Platonic and Archimedean solids are as follows: OptLatPack.pdf.

Visualization of the Packing Structures

The three-dimensional structures of the packings can be visualized using the Windows executable antiview.exe (with OpenGLUT.dll in the same directory) developed by Adrian Rossiter. The configuration files of the densest known packings of non-tiling Platonic solids are as follows: Tetrah.tar (for tetrahedra), Icosah.tar (for icosahedra), Dodecah.tar (for dodecahedra) and Octah.tar (for octahedra).

Each .TAR file includes one or several .OFF files which contain the geometrical information of the polyhedral particles in the packings. To view the three-dimensional model of the structures of packings, the following commands should be used:

For tetrahedra: antiview TetrahPack.Super.off

For icosahedra: antiview pack.icosa.01.off pack.icosa.02.off pack.icosa.03.off pack.icosa.04.off pack.icosa.05.off pack.icosa.06.off pack.icosa.07.off pack.icosa.08.off

For dodecahedra: antiview pack.dode.01.off pack.dode.02.off pack.dode.03.off pack.dode.04.off pack.dode.05.off pack.dode.06.off pack.dode.07.off pack.dode.08.off

For octahedra: antiview pack.octa.01.off pack.octa.02.off pack.octa.03.off pack.octa.04.off pack.octa.05.off pack.octa.06.off pack.octa.07.off pack.octa.08.off

One could also simply select all the necessary configuration files (.OFF files) and "drag" them on top of the icon of the executable antiview.exe to see the three dimensional packing structures.

Questions concerning the materials provided here should be directed to Professor Torquato.



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