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From: vps137 on 21 Dec 2009 20:51
On 20 дек, 20:42, kunzmilan <kunzmi...(a)atlas.cz> wrote:
> On Dec 16, 9:53 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > This is what we visualize as an hypersphere. The 4th dimension has a
> > center and is radial. Its radius is growing producing new points on
> > its round surface.
>
> > Albert Einstein said that "the universe is closed in the 4th
> > dimension." But his idea of time got in the way.
>
> > Mitch Raemsch
>
> We can see a point, a line, a triangle, a tetrahedron. These bodies
> have always (n + 1) dimensions.
> Two tetrahedrons connected by their triangle sides form a four
> dimensional body, since it has 5 vertices. In 3 dimensional space one
> axis, e.g. connecting appears inside of the body. We can write the
> distance matrix of trigonal bipyramide, as if in ideal state (4
> dimensional space), all distances between 5 vertices the same, or as
> its best realization in 3dimensional space.
> kunzmilan

Yes, it's interesting to write it.

Let the tetrahedrone points be (1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1).
If we set the 4th node at (0,0,0,sqrt(5)) we get 5th-hedron. To make
the center be on the equal distances we must add sqrt(5)/5 to every
fourth coordinate of the nodes.
From: vps137 on 21 Dec 2009 21:03
On 22 дек, 06:51, vps137 <vps...(a)gmail.com> wrote:
> On 20 дек, 20:42, kunzmilan <kunzmi...(a)atlas.cz> wrote:
>
>
>
> > On Dec 16, 9:53 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > > This is what we visualize as an hypersphere. The 4th dimension has a
> > > center and is radial. Its radius is growing producing new points on
> > > its round surface.
>
> > > Albert Einstein said that "the universe is closed in the 4th
> > > dimension." But his idea of time got in the way.
>
> > > Mitch Raemsch
>
> > We can see a point, a line, a triangle, a tetrahedron. These bodies
> > have always (n + 1) dimensions.
> > Two tetrahedrons connected by their triangle sides form a four
> > dimensional body, since it has 5 vertices. In 3 dimensional space one
> > axis, e.g. connecting appears inside of the body. We can write the
> > distance matrix of trigonal bipyramide, as if in ideal state (4
> > dimensional space), all distances between 5 vertices the same, or as
> > its best realization in 3dimensional space.
> > kunzmilan
>
> Yes, it's interesting to write it.
>
> Let the tetrahedrone points be (1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1).
> If we set the 4th node at (0,0,0,sqrt(5)) we get 5th-hedron. To make
> the center be on the equal distances we must add sqrt(5)/5 to every
> fourth coordinate of the nodes.

must be "...If we set the 5th node at (0,0,0,sqrt(5))..."

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