Math Is Fun Forum

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Angles in a Icosahedron

I am building a wood model of a Icosahedron.

Can anybody tell me how I work out the angle that any two ajacent faces meet?

If you could direct me to formula for this sort of thing I would be happy to work it out for myself.

SoapyJoe

liuv

Member

Registered: 2006-05-14

Posts: 29

Re: Angles in a Icosahedron

138.19 degrees:)

Last edited by liuv (2006-05-19 19:58:06)

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I'm from Beijing China.

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: Angles in a Icosahedron

Thanks  Liuv,

Can you please tell me how you did this?

Soapy

liuv

Member

Registered: 2006-05-14

Posts: 29

Re: Angles in a Icosahedron

O-ABCDE is a part of a Icosahedron.
OA=OB=OC=OD=OE=AB=BC=CD=DE=EA
Since ABCDE is a Regular Pentagon,therefore <EAB=108°.

triangle OAB, OBC, OCD, ODE, OEF are Regular triangles.
let OA=OB=OC=OD=OE=AB=BC=CD=DE=EA=1,
    OF=AF=0.5
then
    BF=EF=sqrt(AB^2-AF^2)=sqrt(3)/2
in triangle EAB

    BE^2=EA^2+AB^2-2*EA*AB*Cos<EAB=2-2Cos108°
in triangle EFB

BE^2=EF^2+FB^2-2*EF*FB*Cos<EFB=3/2-3/2*Cos<EFB
therefore
2-2Cos108°=3/2-3/2*Cos<EFB
<EFB=138.19° 

Last edited by liuv (2006-05-19 23:16:11)

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I'm from Beijing China.

Evan

Guest

Re: Angles in a Icosahedron

I am building a wood model of a Icosahedron.

Can anybody tell me how I work out the angle that any two ajacent faces meet?

If you could direct me to formula for this sort of thing I would be happy to work it out for myself.

SoapyJoe

Hi joe!  We're you ever able to figure out the adjacent angles?  I'm building an icosahedron out of one inch thick wood, so I wanted to know what angles to cut the adjacent edges.  Nt help would be greatly appreciated!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Angles in a Icosahedron

hi Evan,

Welcome to the forum. 

I had to search back but I remembered this has come up in another thread.

Have a look at

http://www.mathisfunforum.com/viewtopic.php?id=16061

post 30 if you want the method or

http://en.wikipedia.org/wiki/Table_of_p … ral_angles

if you just want to look them up.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Evan

Guest

Re: Angles in a Icosahedron

Thanks, Bob!