Integrate Johnson solids dataset

[lkastner]

This project is part of MaRDI TA1 and the OSCAR project of the SFB-TRR 195.

The Johnson solids are a set of 92 polytopes. A vertex description of these has been notoriously hard to obtain, especially one that can be used by software, as many of these cannot be realized over the rational numbers. Now such a description is available at zenodo and it should be made findable via the portal. I have identified the following subtasks:

• Add description of project to the MaRDI RDM examples page
• Link dataset in wikipedia page
• Add links to single files to the single files of the Johnson solids in both wikipedia and wikidata. Fix bugs in these pages if there are any.

Does that sound reasonable?
cc @zkgeiselmann @alexej-jordan @antonydellavecchia

[zkgeiselmann]

I added a Zenodo Identifier for our description to the wikidata page.
Does this look alright?

[zkgeiselmann]

While adding our Identifiers to the individual Wikidata entries for the Johnson solids, I have noticed an inconsistency.
J1 is a square pyramid, and as a Johnson solid, it has constant edge lengths. In the context of Johnson solids, this last statement is usually omitted.

Wikidata has two competing entries:

1. https://www.wikidata.org/wiki/Q1075704 A square pyramid without further constraints, so the edge length is not necessarily constant, however Norman Johnson is stated as the "discoverer" of this object.
2. https://www.wikidata.org/wiki/Q17370383 A square pyramid with equilateral triangle sides. This has very little data to it, much of which has been added by me, but at the moment classified as a Johnson solid.

Clearly the second one is a Johnson solid and the first one is not necessarily. However the pentagonal pyramid https://www.wikidata.org/wiki/Q1154713 is also classified as a Jonson without specifying the constant edge length (there are more such examples), so using the second entry is inconsistent with the other examples.

I would like to state that the first square pyramid is a Johnson solid under the condition that its edge lengths are constant, but I can't find out whether this is possible in Wikidata (if so this could also be done for the other examples). I would also like to remove Norman Johnson as its discoverer (possibly also for some other Johnson solids, because pyramids have been known for much longer).

If this is not possible I am unsure how to proceed. Do I make the second entry a subclass of the first and repeat this process for similar Johnson solids?

[Daniel-Mietchen]

@lkastner @zkgeiselmann It took me a bit to get into the matter, but now I think I can respond to your points:

While adding our Identifiers to the individual Wikidata entries for the Johnson solids, I have noticed an inconsistency. J1 is a square pyramid, and as a Johnson solid, it has constant edge lengths. In the context of Johnson solids, this last statement is usually omitted.

Wikidata has two competing entries:

1. https://www.wikidata.org/wiki/Q1075704 A square pyramid without further constraints, so the edge length is not necessarily constant, however Norman Johnson is stated as the "discoverer" of this object.

2. https://www.wikidata.org/wiki/Q17370383 A square pyramid with equilateral triangle sides. This has very little data to it, much of which has been added by me, but at the moment classified as a Johnson solid.

Clearly the second one is a Johnson solid and the first one is not necessarily.

Indeed.

However the pentagonal pyramid https://www.wikidata.org/wiki/Q1154713 is also classified as a Jonson without specifying the constant edge length (there are more such examples), so using the second entry is inconsistent with the other examples.

I would like to state that the first square pyramid is a Johnson solid under the condition that its edge lengths are constant, but I can't find out whether this is possible in Wikidata (if so this could also be done for the other examples).

I don't think this is currently possible that way, but I have started a discussion to get some input from others.

I would also like to remove Norman Johnson as its discoverer

Done.

(possibly also for some other Johnson solids, because pyramids have been known for much longer).

Yes, feel free to go ahead and adjust as necessary.

If this is not possible I am unsure how to proceed. Do I make the second entry a subclass of the first

Yes.

and repeat this process for similar Johnson solids?

Yes. I think this would be the way to go for now. If the discussion brings up another option, we can reconsider.

If you keep working on this, maybe this query — or variants of it — can be helpful to keep an overview.

[zkgeiselmann]

@Daniel-Mietchen , thank you very much for your help and sorry for answering this late:

I had a look at the discussion. Someone suggested to use disjoint union to specify the condition under which the square pyramid is a Johnson solid. I don't see a straightforward way to implement this and don't want to create any confusion, so I suggest to leave this aside.

I found out that for many Johnson solids, the names are/can also be used to describe larger classes of polytopes whose edges don't necessarily have the same lengths. That includes all (elongated) (bi-)pyramids, cupolas, rotundas and more. I don't think it would be particularly helpful to essentially duplicate all these objects in order to specify their edge lengths.

In the interest of balancing consistency and and simplicity I suggest to create

1. a pentagonal pyramid with equilateral triangle sides as subclass of the pentagonal pyramid,
2. a triangular bipyramid with equilateral triangle sides as subclass of the triangular bipyramid and
3. a pentagonal bipyramid with equilateral triangle sides as subclass of the pentagonal bipyramid,
   since these are the most common polytopes in this list. As an added benefit this would be largely in agreement with the corresponding Wikipedia pages.

And yes, the query was helpful, thank you!