A TENSEGRITY DOME 
BASED ON THE 4 FREQUENCY ICOSAHEDRON                  


The dome shown in photo 30 
is a circuit pattern Tensegrity
based on a 4 frequency icosahedron, 
truncated just below its equator. 
The dome is part of the figure shown in photograph 10, 
though a few minor alterations have been made 
to the bottom of the dome 
since the complete sphere can't be used. 

The dome is 9'-9" in diameter and 6'-0" high.
This dome is built with 1/2" dia. dowels, 
lock wire for tendons and plastic connectors. 
Stainless Steel safety lock wire, 
a wire used to prevent nuts from vibrating loose on aircraft, 
is used for the tendons, 
as it is easy to build, 
is very strong and does not stretch much. 
Piano wire is very difficult to bend 
and other types of wire are often to ductile 
or else break to easily. 
Ropes and strings tend to be too elastic for large structures. 
This figure has struts of 2 lengths, 
the longer being 36" and 3 different tendon lengths. 
All of the connectors are 2-way connectors, 
except for ten 1-way connectors and ten 3-way connectors 
around the base of the figure.

Diagram 8.8 shows a schematic view 
of the dome from the top. 
In order to show all the components in the diagram, 
a certain amount of distortion has been necessary. 
The center of the diagram represents the apex of the dome 
and the outer edge represents the base. 
Two concentric circuits of lines 
can be traced around the outside of the figure; 
they represent 2 circuits of struts, 
the outer one of which lies directly beneath the inner one. 
The shorter struts are shown as solid 
and the longer ones in outline 
and it can be seen that the 2 kinds of struts 
alternate around the figure 
first the long one then the short one and so on. 
To avoid making mistakes when assembling the figure, 
it is worth coding the struts 
by marking the ends of the shorter ones black
and the ends of the longer ones white, 
then a black end and a white end
will meet at each plastic junction. 
The truncation of the sphere 
causes there to be 10 half-struts, 
of 2 different lengths, 
around the base of the figure. 
Each half strut joins with 2 of the struts 
of the base circuit at a 3-way plastic connector. 
The 1-way plastic connectors 
are used for fixing tendons the other struts 
around the base circuit. 
There are tendons of 3 lengths, 
denoted in the 
diagram by the letters L (Long), M (Medium) and S (Short). 
They follow the sequence  
of long, medium, short, long, medium,... 
round the figure, 
the shortest tendons 
defining the edges of the pentagons 
and the long tendons 
defining the edges of equilateral triangles.
    
The figure is built 
by forming a pentagon 
and adding components symmetrically 
till the figure is complete. 
It is a good idea to support the structure on chairs 
while assembling it, 
to take some of the strain off individual components 
and to save bending over to work.
While assembling the structure, 
a few struts should be added first 
and then as many tendons 
connected as possible 
before adding more struts. 
Some people are tempted 
to try to layout all the struts first, 
using the assembly diagram, 
but they invariably end up 
with a confusing bundle of struts, 
which get in the way when the 
tendons are being fixed. 
As with the mast of the cuboctahedra, 
construction can be speeded 
up by using sticks to measure the lengths of tendon. 
The sticks should be clearly marked, 
as well, to avoid confusion. 
Once the figure has been completed, 
it will be found that 
its base can be pushed out of shape 
because the figure is not a complete system, 
but this can be prevented 
by fixing the base to the ground 
or by running cables 
from the center of the base 
to each of the 3-way connectors. 
Any slack tendons can then be tightened, 
using the techniques described 
for the mast of the cubocthedra.

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