Math Is Fun Forum

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Dihedral angles for a truncated icosahedron

I am very new to this forum so no rocket science please.

I am making wooden models of various shapes and need to be in a position to accurately work out the angles between the planes.

I have previously constructed hardboard models from 'nets' then roughly measured  the angles .... now I would like to know a little more precisely the angles.

Soapy

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Dihedral angles for a truncated icosahedron

If you're making an icosahedron, it's not too hard, I've done it before.  First, cut out equalaterial triangles, all the same size.  Then find a bowl, but you have to be careful that it is the right depth.  You just find this through trial and error.  Place the trangles so that one vertex is in the center (the bottom) of the bowl and the opposite edge of the triangle is resting on the side of the bowl.  If you find a bowl of the right size, they will line up just about perfectly.  Place glue where ever two triangles meet.  The great thing about this method is that you are glueing the inside of the icosahedron, so you can be as messy as you want.

I did it for a biology project.  We were making a T4 bacteriophage virus, which has the head of an icosahedron.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: Dihedral angles for a truncated icosahedron

Thanks Ricky,

Making the full icosahedron is O.K. by the method you describe.... it is quite an  ingenious method.... Thanks.

However, I want to make a truncated icosahedron which is made up of pentagons and hexagons.... I have read about it being described as a 'Buckyball'.

But thanks for replying.

soapy

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Dihedral angles for a truncated icosahedron

All I remember about "buckyballs" is that they are a special molecule called Buckminsterfullerene.

I found a page from Wikipedia: http://en.wikipedia.org/wiki/Fullerene

And it is indeed a truncated icosahedron! The same as a soccerball (if the soccer ball had flat surfaces).

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman