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[2]}, {Sqrt[2], 0, 0}, {0, Sqrt[2], 0},
{0, 0, -Sqrt[2]}, {-Sqrt[2], 0, 0}, {0, -Sqrt[2], 0}}
Show[Polyhedron[Octahedron]]
Or better yet
<< RealTime3D`;
Show[Polyhedron[Octahedron]]
<< Default3D`
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> -----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
> quadrilaterals.
> 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.
>
>
>
>