Octet truss
The octet truss seems to be the one and only most natural/simple/elegant way to fill space with a space-truss.
"Space-truss" means the nodes of the structure only receive tension or compression. They do not experience any bending or torsional loads.
This is unlike space-frames which allow receiving such loads and have the need to provide counter-moments to these loads by bigger stiffened nodes.
- The struts of the octet truss go into the 110 crystallographic directions.
- There are six 110 directions thus there are no less than 12 struts meeting at a fully connected node.
- The voids of the truss (taking the struts as the edges of polyhedra) form octahedra and tetrahedra in a space filling way
- Neither of these two platonic polyhedra (octahedra and tetrahedra) can fill space on their own.
- Octahedra and tetrahedra are deltahedra (like icosahedra nut unlike cubes and dodecahedra). Deltahedra are minimal viable space trusses one could say.
- Fully connected nodes are statically overconstrained which makes octet truss based structures even stiffer.
- Using the nodes as centers for voroni cells one gets rhombic dodecahedra as voroni cells in other words …
- … the nodes of an octet truss are arranged in a face centered cubic fcc pattern.
Interesting but practically little relevant consequence: One can make octet truss struts out of many small rhombic dodecaherdra.
This relation to the octet truss may perhaps in some way be a factor that
makes rhombic dodecahedra of especial interest as shape for microcomponents.
Truncated octahedra (bcc) feature less sharp corners though.
Truncating of the sharper set of corners of rhombic dodecahedra leaves small cube shaped voids in the space-fill which may be acceptable.
Related pages: Sharp edges and splinters; Splinter prevention
