# Talk:Dehn invariant

So what is the Dehn invariant of a regular tetrahedron ? Can we show it as a vector or tensor ? - Rod57 (talk) 10:40, 8 November 2017 (UTC)

  
    
      
        6
        ℓ
        ⊗
        arccos
        ⁡
        
          
            
              1
              3
            
          
        
      
    
    {\displaystyle 6\ell \otimes \arccos {\tfrac {1}{3}}}
  
, where 
  
    
      
        ℓ
      
    
    {\displaystyle \ell }
  
 is the edge length. —David Eppstein (talk) 18:19, 8 November 2017 (UTC)

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Anyone know if this recent proof is accepted? I don't have access to journals. https://link.springer.com/article/10.1134/S0081543818060068
If so we should update this page and the one on flexible polyhedra.  — Preceding unsigned comment added by 67.188.115.54 (talk) 07:59, 2 November 2019 (UTC) 

I was asked to create this image as an illustration for this topic. Not sure if it would make sense in the article, so I propose it here. --Watchduck (quack) 10:34, 24 August 2021 (UTC)

It's a dissection, but there's already an illustration of a dissection in the article and I'm not convinced we need two. In some sense it's more relevant than the 2d dissection already used as an illustration because it's 3d, and this article is mostly about 3d dissection, but on the other hand I think the dissection that it depicts may be too simple to get the point across. Maybe an equilateral-triangle prism instead of the right-isosceles triangle prism? I did add your illustration to Hilbert's third problem, though, because it was lacking any illustration. —David Eppstein (talk) 17:07, 24 August 2021 (UTC)

When Dehn invariant is calculated for the set of 5 Platonic solids, the dihedral angle of dodecahedron in this article is said to be
2atan(2) which is approximately 126.9 degrees.
However, on the page "Regular Dodecahderon" the dihedral angle of the same solid is said to be
acos(-1/sqrt(5)) which is roughly 116.6 degrees. 
Those values are incosistent, and it seems like the second is correct. Am I missing something? Serpens 2 (talk) 05:34, 24 July 2023 (UTC)

I think you're correct. If we're using a formula like 2 atan x, x should be the golden ratio, not 2. —David Eppstein (talk) 05:58, 24 July 2023 (UTC)