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MathGroup Archive 2000

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Re: Need help defining an Octahedron

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24643] Re: Need help defining an Octahedron
  • From: Bob Harris <nitlion at mindspring.com>
  • Date: Mon, 31 Jul 2000 09:23:16 -0400 (EDT)
  • References: <8lt1kp$2l9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I recently posted:
> I'm a novice at Mathematica, and am trying to describe to it a particular
> octahedron.  Any help/suggestions anyone has, I'd be grateful.
> 
> The object's eight faces are four regular pentagons and four quadrilaterals. A
> flat diagram of the object, which can be folded and taped to make the surface
> of the object ... The four pentagons ... are strung from left to right in an
> up/down/up/down pattern;  ...

No further help needed.  I figured out that the object can be described by
these vertices (normalized so that the longest diameter is 2):

        a : <   0  ,   t  , -v >
        b : <   0  ,  -t  , -v >
        c : <  -s  ,  1/2 , -u >
        d : <  -s  , -1/2 , -u >
        e : <   s  , -1/2 , -u >
        f : <   s  ,  1/2 , -u >
        g : < -1/2 ,   s  ,  u >
        h : < -1/2 ,  -s  ,  u >
        i : <  1/2 ,  -s  ,  u >
        j : <  1/2 ,   s  ,  u >
        k : <  -t  ,   0  ,  v >
        l : <   t  ,   0  ,  v >
where
        s = .78615137775742328607
        t = .30028310600077760789
        u = .43701602444882107080
        v = .97719753792427397800

The faces are:
        A : < c,d,h,k,g >
        B : < d,b,e,i,h >
        C : < e,f,j,l,i >
        D : < f,a,c,g,j >
        E : < a,b,d,c   >
        F : < h,i,l,k   >
        G : < b,a,f,e   >
        H : < j,g,k,l   >




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