New Approach

8 11 2008

I have successfully calculated the icosahedron inside the dodecahedron using an a simple formula and some ugly brute force.

Here is how I did this:

Starting with the vertices of a unit dodecahedron, I find the midpoint of each pentagon in the dodecahedron which defines the icosahedron. Given the vertices of each pentagon, you can easy find the midpoint by averaging the points in the pentagon. EASY!

What’s not as easy is grouping the vertices of the dodecahedron into pentagon faces. I used some ugly brute force to find this:

I tested every combination of 5 vertices to find the ones farthest from the center. These vertices define the related icosahedron.

Here we see the tori defined by the icosahedron nested inside the vertices of the dodecahedron:

 

polywell_dodec

Now we can just solve for the midpoint of each edge of the dodecahedron. Here are the edges:

polywell_dodec2

Advertisements

Actions

Information

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




%d bloggers like this: