Talk:Binary icosahedral group

SL(2,5)
Am I right in thinking that this group is isomorphic with the Special Linear group SL(2,5)? If so, is it worth mentioning in the article? Maproom (talk) 14:16, 6 August 2009 (UTC)
 * It is mentioned at Binary icosahedral group. It could fruitfully be mentioned in the lead as well. JackSchmidt (talk) 14:42, 6 August 2009 (UTC)

So as to avoid coming across as highly offensive ...
So as to avoid coming across as highly offensive ... do not use notation that even experienced mathematicians won't necessarily recognize, since in that case most readers of this article will not have the vaguest idea what you mean and then you will have wasted a lot of people's time.

I'm talking about (2,3,5). Can you please say what notation you are using so someone unfamiliar with it can at least look it up? Just because you know about Schwarz triangle groups doesn't mean other readers do. Or maybe encyclopedia articles are not ideal essay subjects for some people interested in writing.2600:1700:E1C0:F340:E94A:D68C:C293:1E78 (talk) 02:51, 29 April 2019 (UTC)

What is phi?
In the "Properties"-section, there is a presentation of the group, and the symbol for the greek letter phi there is a different symbol for the phi in the "Elements"-section. I'm assuming that should be the same phi, but I do not know. Could someone unify/correct/elaborate this? 137.250.162.110 (talk) 14:45, 30 May 2023 (UTC)

Contradictory claims
In the first paragraph of the section "Isomorphisms", it is claimed that "the icosahedral group is isomorphic to the symmetries of the 4-simplex". This is impossible since the second group is twice as large as the first one.

On the other hand, the icosahedral group is indeed isomorphic to the group of rotational symmetries of the 4-simplex, since both are isomorphic to the alternating group A5.

Later in that paragraph it is stated that S5 is not isomorphic to the binary icosahedral group but rather to the "full symmetries" of the 4-simplex.

Apparently someone erroneously believes that the word "symmetries" does not mean the full symmetry group.

I hope someone familiar with English and this subject can fix this.