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[BobbyRobby]

I have to construct a 3D model of a 4D Octahedron. I'm having a lot of trouble finding any pictures to use as reference. Could anyone point me to a site which has such things?

Or better yet, could someone explain how to go about constructing one.

 

[tenchir]

I have to construct a 3D model of a 4D Octahedron. I'm having a lot of trouble finding any pictures to use as reference. Could anyone point me to a site which has such things?

Or better yet, could someone explain how to go about constructing one.

4D?? So it's length, width, depth, and......... time?

I used google and clicked on the first link.

http://astronomy.swin.edu.au/~pbourke/polyhedra/platonic4d/

Here's what I found:

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Cross Polytope
Also known as 16 cell or hexadecachoron

Dual with hypercube

4D equivalent of the octahedron

16 tetrahedral cells, 32 triangular faces, 24 edges, 8 vertices

4 tetrahedra meet at an edge

The generation sequence is: Point - Line - Square - Octahedron - Crosspolytope
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Just use google, I found a lots of pics and info on 4d octahedron.

 

[JoshuaJSlone]

4D?? So it's length, width, depth, and......... time?

Not necessarily time. One can imagine a theoretical fourth spatial dimension that we're just not well equipped to deal with. I'm not sure if there's a standard convention about what to call a fourth to go along with "length" and the rest, though.

Looks like you and Google have done a nice job of providing help, tenchir. I've read up a bit on this stuff, but not enough to help a great deal. I remember the basic idea of creating a 3D model of a 4D shape is analagous to how we often see 3D shapes turned into 2D versions of themselves for display on our limited monitors. And as is the case with a 3D shape being viewed on a 2D screen, what that lower-dimensional representation will look like can differ a lot depending on the viewing angles.

 

[WHOAguitarninja]

I usually just refer to any extra dimensions not easily described as physical aspects (ie: time, density, some sort of tempreture gradient, etc) as sub-dimensions. They're actually kindof fun to play around with in math.

 

[Scrow]

I usually just refer to any extra dimensions not easily described as physical aspects (ie: time, density, some sort of tempreture gradient, etc) as sub-dimensions. They're actually kindof fun to play around with in math.

whoa, slow down there. you can't use the words "fun" and "math" in the same sentence.

 

[slayn]

whoa, slow down there. you can't use the words "fun" and "math" in the same sentence.

what about:

integral(e^x)=f(u^n)

if you write it out, this mathemtical formula spells out sex=fun

 

[BobbyRobby]

Thank you tenchir. The black wire-frame pic helped me out quite a bit.

If anyone is interested in the subject, this site has 4D models you can rotate and distort.

http://www.warren-wilson.edu/~fsolomon/ZZ4DPoly.html

 

[sc0la]

Fun with Calbi-yau spaces

6D pwnage