Math Is Fun Forum

jesseherring

Member

Registered: 2011-07-26

Posts: 19

dihedral angle confusion????

Wondering if anyone can explain/confirm my understanding of dihedral angles relating to woodworking.  as an example, if we are talking about a truncated icosahedron, the published dihedral angles are:
                  hexagon-hexagon face: 138.1896851
                  hexagon-pentagon face: 142.6226319

      Now these are the face to face angles for each of the two required polygons making up the faces of the truncated icosahedron.  If I want to construct a wooden model with 20 hexagons and 12 pentagons made of square sticks, how do I find the required bevels on the hexagons and pentagons? (see attached figures)  After a LOT of confusion I think this is one way to do so. 
      First, take the hexagon-hexagon face and divide in half which gives 69.09....  then subtract this from 90 to get the required bevel angle on the hex-hex sides of each hexagon.  This will be 20.9.....
      Doing the same for the hexagon-pentagon faces gives a bevel of 18.68.....

      Is this the correct method to find these angles?  PLEASE HELP!!!

thanks

jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: dihedral angle confusion????

the required angles?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: dihedral angle confusion????

hi jesseherring,

The dihedral angle is the angle between the faces.

So halving it to get half the bevel on one piece and half on the other, sounds the right thing to me.

You seem to have worked out your own method; well done.:)

You are subtracting from 90, because of where you want to measure from, I presume?

I've never tried anything like this; my woodworking skills wouldn't be up to it. 

So I think to be sure I'd make some pieces and try it out.

Bob

Last edited by Bob (2011-08-28 23:07:53)

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jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: dihedral angle confusion????

bob,

   subtracting from 90 because this is the "default" setting for the saw blade. (both table saw and band saw; 90 degrees = straight cut).