6 Trusses: Twenty-one Zone System

6 Trusses: Twenty-one Zone System

6.1 6 $A$ Lines 15 $C$ Lines

Figure 6.60: Single 21-zone $A$ cell

Figure 6.61: 2 $A$ cells

Figure 6.62: 4 $A$ cells

Figure 6.63: 8 $A$ cells

Figure 6.64: Truss turning corner 8 $A$ cells

Figure 6.65: Truss turning corner 8 $A$ cells - 4 $B$ cells

Figure 6.66: Truss forming arch* $A$ cells middle sections $B$ cells on sides

Figure 6.67: *Truss forming arch Head on view

Figure 6.68: Single 21 zone B cell

10 21-zone truss forming a cap over 5 six-zone diamonds

Figure 6.69:

Figure 6.70:

Figure 6.71:

Figure 6.72: Six-zone truss covering the top half of triacontahedron

Figure 6.73: Pentagonal structure formed by truncating pent corner of triacontahedron. See structure in Figure 15.162

Figure 6.74:

Figure 6.75: Rectangular truss - folded plate configuration

Figure 6.76: Truss formed of obtuse cells.

Figure 6.77:

Figure 6.78: Two views of a rectangular trussed roof.

Figure 6.79: Triacontahedronwith interior icosadodecahedron for stiffening.

6.2 Triacontahedron

22Radius to acute angled corner $= 𝐴𝑇$ . Radius to obtuse angled corner $= 𝐵𝑇$ .

Figure 6.80: Triacontahedron

24 An enneacontahedron within a triacontahedron. The six sided vertices of the enneacontahedron coincide with the three sided vertices of the triacontahedron.

Figure 6.81: Enneacontahedron within a triacontahedron

26 Triacontahedron with edge $= A$ fused with Triacontahedron with edge $= A T^{- 1}$ .

27 Short diagonals of large diamond faces appear as long diagonals of small diamond faces.

28 The acute angled vertex of a large triacontahedron is located at the center of a small triacontahedron.

Figure 6.82: Enneacontahedron within a triacontahedron

30 Triacontahedron clustering carried from $A$ to $A T^{- 2}$ .

Figure 6.83: Triacontahedron