# Talk:5-simplex

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Field: Geometry

## Counting triangles

How would one go about counting the triangles that can be written within the hexateron or K6 complete graph? Someone said it's 117, but I'd like it mathematically verified.

## Complete graph

Why doesn't the article say anything about complete graphs? http://en.wikipedia.org/wiki/Complete_graph http://sl.wikipedia.org/wiki/Slika:Complete_graph_K6.svg

## Cartesian coordinates

In the article, you can read: "For example, the Cartesian coordinates for the vertices of a hexateron (not centered in the origin!), with edge length equal to 2 \sqrt{2}, may be:" I think it's actually centered in the origin. Might it be spam or vandalism? --Daniel bg 16:47, 28 February 2007 (UTC)

However, it was already in the first edition. Can someone explain me this? --Daniel bg 16:52, 28 February 2007 (UTC)
I didn't add the coordinates, but easy to check - all vertices should be equal distance from all others. Definitely not centered on origin in 4th and 5th coordinates since they're all positive. Tom Ruen 00:02, 1 March 2007 (UTC)

## corruption of "tetra"

Somehow this doesn't sound like a good way to word it. I think the article should explain that "tera-" was from the SI prefix. 4 T C 03:18, 21 February 2010 (UTC)

## "hexa-5-tope"? really?

Does hexa-5-tope imply that 5-tope is a cromulent word? If so, then what about (and why not) hexatope or, if you insist, 6-tope? —Tamfang (talk) 05:53, 16 September 2010 (UTC)

5-tope is short for 5-polytope short for 5-dimensional polytope[1], the only other choice I've seen (that specifies a dimension) for people who don't want to use -teron. Really you might say poly-5-tope in general and then hexa-5-tope for the 6-faceted 5-simplex. Hexatope doesn't imply dimension and could also mean a hexagon, hexahedron or hexachoron (pentachoron frustum?). Tom Ruen (talk) 20:51, 16 September 2010 (UTC)
But it doesn't consist of six 5-polytopes.
I may have previously mentioned that I disapprove of using hedron ('face') as if it meant polyhedron ('[thing with] many faces'). I likewise disapprove of using tope ('place') as if it meant polytope ('[thing consisting of] many places'). —Tamfang (talk) 11:05, 23 September 2010 (UTC)
Hmmmm... not sure what to do with disapproval. As defined, an n-polytope means a polytope in n-space bounded by (n-1)-facets. But what about an n-honeycomb? Is a tiling a 2-honeycomb and an infinite 3-polytope? But, in comparison, 3-sphere is a 3D surface in 4D. Tom Ruen (talk) 18:21, 23 September 2010 (UTC)