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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, three-way 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	three-way 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 Tri-1 spaceframe, or octet truss.

One of the first practical uses of the octet truss lattice was a man-carrying 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 Tri-1 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 two-way square lattice, called
	the Square-2 spaceframe, which is a slice taken parallel
	to the 100 plane. The other is a two-way rectangular
	lattice, Rec-2, which is sliced parallel to the 110 plane.

	Fig. 230 - Slicing the octet truss (blue) to reveal the Tri-1
	(purple), Square-2 (red), and Rec-2 (green) spaceframes

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