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Posted: Fri Oct 05, 2012 11:08 am
I am building polyhedra in wood. To build a Rhombicsidododechedron the square sections the miters alternate between 15.857 and 10.4526 degrees. I have built several dozen of these and set my saw to these angles and it worked great..Dead on the money..
However, I read Magnus Wenninger's book "Spherical Models" and his Rhombicsidododechedron does make the same allowance....All sides of his square sections are the same mitre..
What am I missing..?
Posted: Fri Oct 05, 2012 12:11 pm
I don't think you're missing anything. Stella reports the same mitre angles that you use. Maybe Magnus divides the dihedral angle differently, not equally. You could use the same angles all around the squares if you adjust the angle on the connecting part. The alignment wouldn't quite match on the inside though.
Posted: Fri Oct 05, 2012 12:22 pm
I understand what you are saying about dividing the dihedral angles. However, I am still perplexed. If you subtract from one Dihedral angle you have to add that to it's matching component. Thus, one side is going to be shorter and the other longer. Thus, the inside radius must change accordingly. Magnus makes no such allowance that I can see. All his radaii are the same.
I used his computations and built one. It seemed to fit but paper is much more forgiving than wood..
I guess I will have to calculate his dihedral angles or as the case may be work backwards to see??
Posted: Fri Oct 05, 2012 12:56 pm
I my last post I forgot to thank you for your help..!! I have some pictures I would like to send you. Can I send them direct to you wiht out posting them? Once you look at them you are welcome to post them on your site.
Posted: Fri Oct 05, 2012 2:25 pm
It's probably just a mistake in Magnus's book.
How did you test a mitre angle with paper??
Yes, you can email pictures to me, or if you have them hosted online somewhere you can post them yourself on these forums. You can open a free photobucket.com account to host images if you wish.
Posted: Fri Oct 05, 2012 2:32 pm
I did not test the miter in paper. I have built about two dozen in wood. This is the empircal test. Wood is not forgiving..