CIRCUIT PATTERN  SYSTEMS 
BASED ON THE GEODESIC POLYHEDRA 
OF R. BUCKMINSTER FULLER                                                               


Larger circuit- pattern systems 
must be based on larger polyhedra 
such as the geodesic polyhedra developed by Fuller.
There are many different families of polyhedra, 
but this discussion will only involve certain figures 
derived by the alternate method. 
See discussion of methods elsewhere in this paper.

GEODESIC POLYHEDRA 
AND THE CIRCUIT PATTERN 

Since four tendons, 
defining four edges of of a polyhedron, 
meet at each vertex of a circuit pattern, 
and since six edges meet 
at most of the vertices 
of these geodesic polyhedra, 
it is difficult at first 
to see how circuit pattern Tensegrity systems 
can be based on them.
The difficulty is made worse 
by the fact 
that circuit-pattern Tensegrity figures 
can not be based on all geodesic polyhedra. 
Fortunately, 
there are a few simple rules to clarify the issue,
Circuit-pattern Tensegrity systems 
can be based on any geodesic polyhedron 
derived by the alternate method, 
provided that the faces of the principal polyhedron 
have been subdivided 
to a frequency which is a multiple of 2.  
The sketches in diagram ___ 
show a triangular face of a principal polyhedron 
subdivided into various frequencies. 
The edges of the original triangles 
are shown 
in slightly heavier line 
than the lines which subdivide each face. 
Over each face appear, 
in very heavy line, 
the paths taken by the struts & tendons in the circuit-pattern figures.
This pattern, 
a tessellation of hexagons & triangles, 
can't be superimposed symmetrically over a face 
which has been subdivided 
to a frequency which is not a multiple of 2. 
Hexagons occur along the edges 
of the original triangles, 
half on one triangle 
and half on the adjacent triangle. 
The circuits may also define faces
other than hexagons & triangles 
about the vertices  
of the original triangles 
of the principal polyhedron, 
as is apparent in the following examples. 
See detail ____ .
Next, 
one must relate the individual struts & tendons 
to the circuits established in diagram _____ . 
Diagram ___ shows the struts & tendons 
sketched onto triangles of a principal polyhedron 
divided to various frequencies. 
It can be seen that the struts and the tendons 
follow the same lines 
as the circuits identified in diagram 5.4  
and that the circuits of the struts 
interweave one another, 
{just as they did in the systems described in Ch. 4. }

EXAMPLES

Having discussed the basic principals, 
it is worth studying a few examples.
The heavier lines in the following sketches 
show the paths of the circuits of struts and tendons round the figure 
and the lighter lines show the edges 
generated by the edges of the principal polyhedron (the icosahedron).
The broken lines show the other edges of the geodesic polyhedron.
The 2-frequency icosahedron is the icosidodecahedron described 
in ch. 4. The tensegrity shown in photograph 6 
has 30 struts which form 6 pentagonal interweaving circuits 
and 60 tendons which define the edges of an icosidodecahedron. 
All struts of this figure can be the same length 
and all the tendons equal in length.
The figure based on the 4-frequency icosahedron (diagram ___ )
has 120 struts arranged in 12 interweaving decagonal circuits 
and 240 tendons, as shown in photograph 10. 
Since geodesic polyhedra are not as regular 
as the Archimedean polyhedra, 
this figure will usually have struts of 2 different lengths 
and tendons of 3 different lengths. 
Instructions for building a model of this figure will be given later.
The figure based on the 6-frequency icosahedron (diagram ___ ) 
has 270 struts and 540 tendons as shown in photograph __ . 
It has 18 circuits which interweave without touching one another. 
Each circuit contains 15 struts, 
but there are 2 different types of circuit, 
as there are usually struts of 5 different lengths 
in 2 different sequences round the figure. 
There are usually tendons of 6 different lengths. This figure can be built 
in exactly the same way as the other circuit-pattern figures , 
but it takes a long time to build, 
simply because it has so many components.
By now the basic idea should be apparent, 
and it is worth briefly looking at a wider range of figures. 

GENERAL NOTE ON THE CONSTRUCTION OF MODELS

It takes a long time 
to build the larger examples 
of this type of figure,
simply 
because of the number of struts and tendons involved.
Fortunately 
as much can be learned 
from the smaller figures.

FINAL NOTES

There are enormous numbers of geodesic polyhedra 
on which Circuit-Pattern Tensegrity systems 
can be based. 
This discussion has only described a few systems 
based on figures derived by the alternate method 
from a few principal polyhedra, 
but there are many other ways 
of subdividing principal polyhedra, 
and there are many other polyhedra 
which can be used as principal polyhedra. 
In addition,
these Circuit-Pattern Tensegrity systems 
are not regular, 
and many variations can be made 
in the geometry of each figure. 
It is hoped that this chapter 
together 
with the assembly instructions in subsequent chapters, 
explain enough of the basic ideas and techniques 
to allow the reader to work on other figures of this type. 


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