4d pyramids

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4d pyramids

Postby batmanmg » Mon Aug 28, 2006 5:18 am

ok you can make a triangle by starting with one line then putting infinity progesively smaller lines next to it in the 2nd dimension. you can make a pyramid by starting with a square and putting infinity progresively smaller squares on top of it in the 3rd dimension...

but what about putting together a 4d pyramid... is it like the cube shifted in the 4d to make a tesseract, only when its shifted it gets progressively smaller? in essence like stacking infinent progressivly smaller cubes in the 4th dimension?

if so what would a 4d pyramid look like?
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Postby moonlord » Mon Aug 28, 2006 9:43 am

A pyramid is generally any body formed by tapering to a point -- the process you described. For example, the triangle is the line pyramid. And yes, there is that cube pyramid, but every 3D body can be tapered to form a 4D pyramid. So you have the cilinder pyramid and so forth.
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Re: 4d pyramids

Postby pat » Mon Aug 28, 2006 6:40 pm

batmanmg wrote:ok you can make a triangle by starting with one line then putting infinity progesively smaller lines next to it in the 2nd dimension. you can make a pyramid by starting with a square and putting infinity progresively smaller squares on top of it in the 3rd dimension...


Sure, but you could also make a 3-d pyramid by starting with a triangle and putting infinitely many, progressively smaller triangles on top of it in the 3rd dimension. This is a tetrahedron, the simplest of pyramids. It's also the simplest of polytopes and is, unsurprisingly, called the simplex.

Now, you can take a tetrahedron and stack infinitely many, progressively smaller tetrahedrons on top of it in the fourth dimension to get the 4D simplex.
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Postby moonlord » Mon Aug 28, 2006 6:48 pm

...and this stacking is essentially what the taper-to-a-point operation is. The operation that creates all kind of pyramids...
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