Filling Space with Tetrahedra and Half-Size Octahedra

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Four tetrahedra are arranged around a half-size octahedron. This arrangement is repeated to form a space filling structure with alternating layers of tetrahedra and octahedra.
Contributed by: Sándor Kabai (June 2016)
with additinal contributions by Dániel Erdély
Open content licensed under CC BY-NC-SA
Snapshots
Details
Dániel Erdély told me about the tetrahedron arrangement; his father made a model of it years ago. Without octahedra, the space filling ratio of tetrahedra is 2/3, as explored by a number of authors including John Conway and Klee Irwin.
Reference
[1] J. H. Conway and S. Torquato, "Packing, Tiling, and Covering with Tetrahedra," Proceedings of the National Academy of Sciences, 103(28) 2006 pp. 10612–10617. doi:10.1073/pnas.0601389103.
Permanent Citation
"Filling Space with Tetrahedra and Half-Size Octahedra"
http://demonstrations.wolfram.com/FillingSpaceWithTetrahedraAndHalfSizeOctahedra/
Wolfram Demonstrations Project
Published: June 2 2016