Lines and Connectivities Problem

Hey all,

Currently I am trying to make model consist of bars (i.e: each bar should contain only 2 nodes). I wanted to make those bars from the tessellation figure as shown below.

So initially I have the above model (please see Rhino attached file). As can be seen each polygon overlap with another polygon. Then I find the intersection of those polygon  to make it look like below:

Now, what I want is to have bars OR lines with connectivities such as these:

0,2

2,1

1,4

4,26

26,2

4,3

3,5

5,0

0,9

9,7

7,8

8,31

31,9

8,6

6,10

10,0

....

....

and so on

....

So that these connectivities create a set of lines with the connectivities like mentioned above. 

I attached the files below. Please advise.

Thank you very much in advance for your help in this matter.