Talk:26-fullerene graph

dubious, indeed
According to User:David_Eppstein, dubious/reason:The image shows six hexagons/date:May 2018. Let us ask the image again:

GR:= Graph( {{1, 2}, {1, 6}, {1, 7}, {2, 3}, {2, 8}, {3, 4}, {3, 9}, {4, 5},
 * {4, 10}, {5, 6}, {5, 11}, {6, 12}, {7, 13}, {7, 18}, {8, 13}, {8, 14},
 * {9, 14}, {9, 15}, {10, 15}, {10, 16}, {11, 16}, {11, 17}, {12, 17}, {12, 18},
 * {13, 19}, {14, 20}, {15, 21}, {16, 22}, {17, 23}, {18, 24}, {19, 20}, {19, 24},
 * {20, 26}, {21, 22}, {21, 26}, {22, 23}, {23, 25}, {24, 25}, {25, 26}});

IsPlanar(GR, 'faces'); faces; nops(%), map(nops,%);

And the answer is:

$$[[25,26,20,19,24],[22,21,26,25,23],[23,17,11,16,22],[16,10,15,21,22],[11,5,4,10,16],[19,20,14,8,13],$$ $$[13,7,18,24,19],[18,7,1,6,12],[9,3,2,8,14],[6,5,11,17,12],[4,3,9,15,10],[2,1,7,13,8],$$

$$[24,18,12,17,23,25],[21, 15,9,14,20,26],[5,6,1,2,3,4]]$$

i.e.

$$15, [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6]$$

Pldx1 (talk) 09:53, 11 May 2018 (UTC)

Moreover, Weisstein says: Examples include the 20-vertex dodecahedral graph, 24-vertex generalized Petersen graph GP(12,2), graph on 26 vertices given by Gosil and Royle (2001, p. 208), truncated icosahedral graph, and stable molecule C_(70) (Babić et al. 2002), illustrated above.

So what ? Pldx1 (talk) 10:38, 11 May 2018 (UTC)
 * That was a typo. I meant "three hexagons". The article at the time I typed it said two. In general, this illustrates the dangers of original research: when you are calculating properties of something yourself, rather than using any sources (and I know of no in-depth sources about this specific graph) you can easily make mistakes. —David Eppstein (talk) 17:53, 11 May 2018 (UTC)

Fixed dubiousness (mostly)
The reason I was so insistent on tagging this article as dubious is that the former name "Godsil–Royle graph" appears to have been made up by the Wikipedia editor who created the article. There is no prior use of this name anywhere. And any serious look at the history of study of this graph provides no justification for assigning credit to those two authors. In other words, choosing this name was both original research and a mistake. By renaming it "26-fullerene graph" and rewriting it to reflect earlier sources, I have fixed that problem. The problem still remains in the name of the file used as an illustration for this article, though. , can I ask you to please repent of your sin and put in a request on commons to give the file a more appropriate name? Thanks. —David Eppstein (talk) 18:59, 13 May 2018 (UTC)
 * @David Eppstein.please repent of your sin. I'm c-mused. Pldx1 (talk) 11:26, 14 May 2018 (UTC)
 * That's like bemused, only one step up? —David Eppstein (talk) 15:49, 14 May 2018 (UTC)
 * c-mused is {a,be}-mused. Pldx1 (talk) 18:18, 14 May 2018 (UTC)