Talk:Genus-three surface

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First section deleted[edit]

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,
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? (talk) 17:07, 13 February 2014 (UTC)


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[edit]

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)