       Need help defining an Octahedron

• To: mathgroup at smc.vnet.net
• Subject: [mg24635] Need help defining an Octahedron
• From: Bob Harris <nitlion at mindspring.com>
• Date: Fri, 28 Jul 2000 17:24:25 -0400 (EDT)
• Organization: MindSpring Enterprises
• Sender: owner-wri-mathgroup at wolfram.com

```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.

```

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