Triangular spaceframe lattice, Tri1:
(selfdual tessellation, threeway triangular outer grid 
over threeway triangular inner grid) 
. 



◄ Fig. 231  Tri1 spaceframe 
sliced out of the octet truss 

Fig. 232  Strut diagram ► 
(looking down from shove) 
click image to enlarge 

. 
Fig. 232 is a diagram of the layout of the struts comprising the Tri1 spaceframe.
By 
convention the bottom (blue) grid layer is called the inner layer, and the
top (red) grid layer 
is
called the outer layer (as though the spaceframe were enclosing an
interior space). The 
diagonal
struts comprising the web of the spaceframe are colored purple. The
lattice is 
categorized according to the predominant polygonal shape in the pattern of
the outer layer, 
which in
this case is the triangle. The number following the name denotes
each variation 
of the
basic category  hence it is called Tri1. 
. 
You can
use Euler's equation for stable polyhedra, E = 3J  6,
to determine the stability of 
the Tri1 spaceframe by analyzing a section of it called a
unit cell. A unit cell is the smallest 
segment
of the structure that contains all of its basic elements.
Consequently the entire 
lattice can be constructed by simple repetition of the cell (called tiling
the plane). Fig. 233 
is a model of the Tri1 unit cell. It is a rhombohedron comprised of
two tetrahedra and one 



Fig. 233  Tri1 unit cell 
click image to enlarge 
◄ top view 
side view ► 

18 = 3 ( 8 )  6 stable 


octahedron. The cell has 18 members, or struts, and 8 joints, or
hubs. Euler's equation 
predicts that it is inherently stable.
Therefore the Tri1 lattice is
also (obviously, in this 
instance, since the lattice is entirely triangulated). 
. 
The
equation presumes of course that the joints of the lattice are completely
flexible, which 
they
are here. A load applied perpendicularly to the plane of the spaceframe is
dissipated 
axially
throughout the struts as tension and compression stresses. The
individual struts do 
not
experience any significant bending stresses. This is directly
analogous to how statically 
determinate truss bridge designs with pinned joints react to a load. Like
a truss deck bridge, 
the
spaceframe's outer grid of struts, which correspond to the top chord
members of the 
bridge,
are subjected to compressive stresses primarily. And the inner grid
of struts, which 
. 
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Page 135
 Building stability  Tri1 spaceframe 

