Talk:Hesse configuration

Also known as Young's geometry

Some sources refer to this object as Young's geometry, e.g. Finite Geometries by Shubin (2006) . Apparently it's named after John Wesley Young. I can't find an original source for Young, but many sources which use the name "Young's geometry" start from the finite affine plane axioms. Looking at the source here for Hesse, I see more of an algebraic approach. Not totally sure though since I can't read the German. Maybe this points to a subtle difference between the two terms?

Also probably worth noting Young's research somewhere. FionaLovesCats (talk) 19:18, 28 April 2023 (UTC)

I agree with including this name, but it would be good to track down a better source for why it has this name than a web page that says it "appears to be named for" one of many people named Young who wrote about geometry. I think there is a subtle difference in emphasis, but maybe not in mathematical content: as the Hesse configuration, it is generally understood that it can be a subset of the points and of the lines in a larger geometric space (such as the complex projective plane), but as Young's geometry, it is the whole space. —David Eppstein (talk) 21:17, 28 April 2023 (UTC)

I did find a reference to this configuration in the work of Young: Veblen & Young Projective Geometry 1910, p. 249. It's unclear to me whether this publication is the origin of the credit to Young or, if so, why Veblen is omitted. —David Eppstein (talk) 07:30, 29 April 2023 (UTC)

432 automorphisms?

I computed 432 automorphisms (48×9) by brute force 9! point permutations, but article says 216 automorphisms. Any explanation? Tom Ruen (talk) 03:33, 11 April 2025 (UTC)

Block representation of the configuration (9₄ 12₃)

0	0	0	0	1	1	1	2	3	2	4	5
1	2	3	6	2	3	5	3	4	4	7	6
4	5	8	7	8	6	7	7	5	8	8	8

The 216 was added (2016 diff) by @Marozols:

French version says 432: (2024 diff)

• https://fr.wikipedia.org/wiki/Configuration_de_Hesse:
• The Hessian configuration has 432 symmetries. In other words, its automorphism group is of order 432: it is the affine group $\mathrm {GA} _{2}(\mathbf {F} _{3})\simeq \mathbf {F} _{3}^{2}\rtimes \mathrm {GL} _{2}(\mathbf {F} _{3})$ It admits as a subgroup of order two the Hessian group.

- Tom Ruen (talk) 03:42, 11 April 2025 (UTC)