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.

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 Fig. 228 -Tri-1 spaceframe (octet truss) overhead view  ► (static demonstration model) click image to enlarge

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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

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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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