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

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

Hope this helps,
-- Jean-Marc

```

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