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 >