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 >