Spaceframe
lattices 


Two single layer grids can also be stacked on top of each other so 
that the grid pattern of one layer is staggered relative to the grid
of 
the other layer (Fig. 227). The joints of one grid are aligned
with 
the center
points of the polygons of the other grid like dual 
tessellations. As a result the web elements, or struts, form
oblique 
angles with the grids they span between.
Fig. 228 following 
shows an example of two staggered,
single layer, threeway grids 
click to enlarge 
that are connected together with struts to form a completely 
Fig. 227  Staggered 
triangulated lattice structure, or spaceframe. In this
particular 
threeway grids 
spaceframe, all of the struts making up the grid and web of the 


lattice
are of equal length. Each facet, or face, of the lattice is an
equilateral triangle. 
As
a structural framework it is
commonly referred to as a Tri1 spaceframe, or octet truss. 
. 



Fig. 228 Tri1 spaceframe 
(octet truss) 
overhead view ► 
(static demonstration model) 
click image to enlarge 

. 
One of
the first practical uses of the octet truss lattice was a mancarrying
kite invented 

by Dr.
Alexander Graham Bell in 1907. This lattice was also 

popularized later by R. Buckminster Fuller as the isotropic 
vector matrix, or IVM. Readers of the prior lesson on 
geometry will recognize it as a space filling of tetrahedra 
and octahedra in the ratio of two to one respectively. 

◄
Fig. 229  Cygnet tetrahedral kite (Bell,
1907) 
click image to enlarge 

. 
It is
also identical to the FCC crystal lattice structure presented in the
previous lesson on 
crystallography. The Tri1 spaceframe can be cut out of the
FCC crystal lattice by slicing 
it
parallel to the 111 plane. Two other basic spaceframe lattices
can be sliced out of the 

octet truss also. One is a twoway square lattice, called 

the Square2 spaceframe, which is a slice taken parallel 
to the
100 plane.
The other is a twoway rectangular 
lattice, Rec2,
which is sliced parallel to the 110 plane. 

Fig. 230  Slicing the octet truss (blue) to
reveal the Tri1 
(purple), Square2 (red), and Rec2 (green) spaceframes 

. 
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 Building stability  Spaceframe lattices 

