       RE: Need help defining an Octahedron

• To: mathgroup at smc.vnet.net
• Subject: [mg24655] RE: [mg24635] Need help defining an Octahedron
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 31 Jul 2000 09:23:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Bob,

Needs["Graphics`Polyhedra`"]

Vertices[Octahedron]

{{0, 0, Sqrt}, {Sqrt, 0, 0}, {0, Sqrt, 0},
{0, 0, -Sqrt}, {-Sqrt, 0, 0}, {0, -Sqrt, 0}}

Show[Polyhedron[Octahedron]]

Or better yet

<< RealTime3D`;
Show[Polyhedron[Octahedron]]
<< Default3D`

David Park

> -----Original Message-----
> From: Bob Harris [mailto:nitlion at mindspring.com]
To: mathgroup at smc.vnet.net
> Sent: Friday, July 28, 2000 5:24 PM
> To: mathgroup at smc.vnet.net
> Subject: [mg24655] [mg24635] Need help defining an Octahedron
>
>
> Howdy,
>
> 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
> A flat diagram of the object, which can be folded and taped to make the
> surface of the object, is (crudely) shown below (and which must be viewed
> using a monospaced font, such as Courier New or Monaco).
>
> The four pentagons (A, B, C, and D) are strung from left to right in and
> up/down/up/down pattern;  when folded, the lower right edge of D joins the
> upper left edge of A.  The quadrilaterals (E, F, G, and H) then
> fold down so
> that, for example, G has common edges with B, C, D, and E.
>
> :        -         .         -         .
> :       / \     .     .     / \     .     .
> :      / E \  .         .  / G \  .         .
> :     .-----.             .-----.             .
> :    /       \     B     /       \     D     /
> :   /         \         /         \         /
> :  /     A     \       /     C     \       /
> : .             .-----.             .-----.
> :   .         .  \ F /  .         .  \ H /
> :     .     .     \ /     .     .     \ /
> :        .         -         .         -
>
> Beware that the diagram as drawn here misrepresents some of the angles and
> lengths.  In particular, the short sides of the quadrilaterals are longer
> than they appear;  all other side lengths are one unit, but the short side
> has length about .637 (1-2*sin(pi/5)*cos(2*pi/5), but I'm not
> positive that
> this is correct).  The three segments from the top of G through the bottom
> of F (including the BC edge) are *not* colinear.
>
> What I want to do is describe this object to Mathematica without me having
> to figure out where all the vertices end up in three space.  I'm
> looking for
> Mathematica to (somehow) figure out the <x,y,z> coordinates of
> each vertex.
>
> I'd also like for Mathematica to draw it and rotate it, but I think I can
> figure out how to do that once I have the vertices.
>
> Thanks in advance for any help,
> Bob Harris
>
> P.S.  If there is some other tool that would be better suited for
> this, let
> me know.
>
>
>
>

```

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