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Re: Coordinates of vertices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87757] Re: Coordinates of vertices
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 16 Apr 2008 06:52:20 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <ftv8ro$7o1$1@smc.vnet.net> <200804141054.GAA13581@smc.vnet.net> <fu4fga$nes$1@smc.vnet.net>

King, Peter R wrote:

> I am sure I have done this before but I can't for the life of me 
> remember how, and I can't find it in the manual. Some help would be much 
> appreciated. I'd like to find the coordinates of the vertices of a 
> truncated cube.
> 
> Whilst Vertices[cube] correctly gives me the coordinates of a cube 
> Vertices[Truncate[Polyhedron[Cube]]] doesn't do what I want because 
> Truncate[Polyhedron[... is a graphics object not a polyhedron object. So 
> can I convert the graphics object into a polyhedron and use vertices, or 
> work out the vertices some other way (for a cube this is trivial to do 
> but for more complicated shapes this is much more tedious)

Hi Peter,

Assuming I have correctly understood what you are looking for and that 
you are using version 6.x.x, you can get, among many many other things, 
the coordinates of a truncated cube thanks to the PolyhedronData[] 
function. For instance,

In[1]:= PolyhedronData["TruncatedCube", "VertexCoordinates"]

Out[1]= {{-(1/2), 1/2 + 1/Sqrt[2], 1/2 + 1/Sqrt[2]}, {-(1/2),
   1/2 + 1/Sqrt[2], 1/(2 - 2 Sqrt[2])}, {-(1/2), 1/(2 - 2 Sqrt[2]),
   1/2 + 1/Sqrt[2]}, {-(1/2), 1/(2 - 2 Sqrt[2]), 1/(
   2 - 2 Sqrt[2])}, {1/2, 1/2 + 1/Sqrt[2], 1/2 + 1/Sqrt[2]}, {1/2,
   1/2 + 1/Sqrt[2], 1/(2 - 2 Sqrt[2])}, {1/2, 1/(2 - 2 Sqrt[2]),
   1/2 + 1/Sqrt[2]}, {1/2, 1/(2 - 2 Sqrt[2]), 1/(
   2 - 2 Sqrt[2])}, {1/2 + 1/Sqrt[2], -(1/2),
   1/2 + 1/Sqrt[2]}, {1/2 + 1/Sqrt[2], -(1/2), 1/(
   2 - 2 Sqrt[2])}, {1/2 + 1/Sqrt[2], 1/2,
   1/2 + 1/Sqrt[2]}, {1/2 + 1/Sqrt[2], 1/2, 1/(
   2 - 2 Sqrt[2])}, {1/2 + 1/Sqrt[2],
   1/2 + 1/Sqrt[2], -(1/2)}, {1/2 + 1/Sqrt[2], 1/2 + 1/Sqrt[2], 1/
   2}, {1/2 + 1/Sqrt[2], 1/(2 - 2 Sqrt[2]), -(1/2)}, {1/2 + 1/Sqrt[2],
   1/(2 - 2 Sqrt[2]), 1/2}, {1/(2 - 2 Sqrt[2]), -(1/2),
   1/2 + 1/Sqrt[2]}, {1/(2 - 2 Sqrt[2]), -(1/2), 1/(
   2 - 2 Sqrt[2])}, {1/(2 - 2 Sqrt[2]), 1/2, 1/2 + 1/Sqrt[2]}, {1/(
   2 - 2 Sqrt[2]), 1/2, 1/(2 - 2 Sqrt[2])}, {1/(2 - 2 Sqrt[2]),
   1/2 + 1/Sqrt[2], -(1/2)}, {1/(2 - 2 Sqrt[2]), 1/2 + 1/Sqrt[2], 1/
   2}, {1/(2 - 2 Sqrt[2]), 1/(2 - 2 Sqrt[2]), -(1/2)}, {1/(
   2 - 2 Sqrt[2]), 1/(2 - 2 Sqrt[2]), 1/2}}

Hope this helps,
-- Jean-Marc


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