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

**References**:**Re: List concatenation - two more methods, one truly fast***From:*Oliver Ruebenkoenig <ruebenko@uni-freiburg.de>