Wiring Diagram

22 02 2009

So I’m working on an algorithm to come up with a wiring diagram for the dodecahedral core. It’s more complicated than just wiring up the 12 coils in series. This is would only magnetically protect 12 of the 30 connecting joints. Ideally each join would get one pass of superconducting cable. A picture to meditate on:

dodec_net

 

Lets start by making some methods to traverse the net. Currently I have this functionality:

 

 

Geometry::Dodecahedron.faces.first

=> [Vector[1, 1, 1], Vector[1, 1, -1], Vector[0.618033988749895, 1.61803398874989, 0], Vector[1.61803398874989, 0, 0.618033988749895], Vector[1.61803398874989, 0, -0.618033988749895]]

So I can easily iterate through the the faces, and I get the vertices of that face unordered. The first challenge is to order these collections of vertices so that you traverse the face clockwise simply by iterating the collection.
About these ads

Actions

Information

4 responses

19 03 2009
fenn

are you trying to find the hamiltonian path of a dodecahedron?

20 03 2009
FAMULUS

Certainly a step in the right direction. Although we want to visit each _edge_ only once, not each vertex.

http://en.wikipedia.org/wiki/Hamiltonian_path

20 03 2009
FAMULUS

We want the Eulerian_path, which touches each edge exactly once:

http://en.wikipedia.org/wiki/Eulerian_path

20 03 2009
FAMULUS

However!

According to this page

http://mathworld.wolfram.com/DodecahedralGraph.html

The dodecahedron does not have a Eulerian Path!

As a practical matter, this means one or more of the joints (edges) will have more than one transition.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s




Follow

Get every new post delivered to your Inbox.

Join 669 other followers

%d bloggers like this: