# Talk:Genus-three surface

(Redirected from Talk:Triple torus)
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Field:  Geometry

## First section deleted

I have deleted the first section of the article, because I believe it was mostly mistaken.

The three-dimensional torus, or triple torus, is defined as the Cartesian product of three circles,
${\displaystyle \mathbb {T} ^{3}=S^{1}\times S^{1}\times S^{1}.}$
In contrast, the usual torus is the Cartesian product of two circles only.

This can't be right. We are trying to construct a surface, something two-dimensional. The construction defined gives something three-dimensional.

The triple torus is a three-dimensional compact manifold with no boundary. It can be obtained by gluing the three pairs of opposite faces of a cube. (After gluing the first pair of opposite faces the cube looks like a thick washer, after gluing the second pair — the flat faces of the washer — it looks like a hollow torus, the last gluing — the inner surface of the hollow torus to the outer surface — is physically impossible in three-dimensional space so it has to happen in four dimensions.)

I think this construction gives something with the topology of a sphere. Maproom (talk) 15:29, 23 January 2012 (UTC)

Then could you fix the link in Doughnut theory of the universe to what the proposed shape actually is? Is it a "three-dimensional torus" or a triple torus? 166.170.28.2 (talk) 17:07, 13 February 2014 (UTC)

## source?

Is there a source for referring to the 3-dimensional torus as "triple torus"? Tkuvho (talk) 14:49, 11 September 2013 (UTC)

## Two more representations of the triple torus

Is the statement

Just as a torus can be represented as a square with opposite edges identified or as a hexagon with opposite edges identified, a triple torus can be represented as a dodecagon with opposite edges identified or as a 14-gon with opposite edges identified
• obvious or easily verifiable, or
• referenced somewhere, or
• unnacceptable, as "original research"? (comment contributed by User:Maproom)
Doesn't seem entirely obvious. I suggest you look through the history to see who added this comment and ask them for a reference. Tkuvho (talk) 13:27, 12 September 2013 (UTC)
No-one has added it. I would like to, Maproom (talk) 18:31, 12 September 2013 (UTC)