The explanation is clearer. Thanks!

]]>Reading the earlier posts, the update is clearer.

]]>Added the first (much simpler) explanation. Does it read fine? Any mistooks?

]]>... Although there might be some that can only be spotted by advanced topologists ...

Sorry, I couldn't resist taking advantage of that statement.

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In my opinion, that is.

Devanté wrote:

I must be an advanced topologist, then.

Not necessarily. Don't make me go Boolean on you.

]]>Or can you define a set of properties so that any solid that meets them will make F+V-E=2 work?

For all solids that can be "deformed" to the sphere it still holds. So that is an entire class of solids.

Another class of solids can be deformed to a torus, and for them F+V-E=1

I didn't go into on that page, but there is a 2D equivalent of F+V-E=2, and it is V-E=0

And the 1D version is V=2

In fact it goes like this for "non intersecting" shapes:

0D: 0

1D: V=2

2D: V-E=0

3D: F+V-E=2

4D: F+V-E-(something)=0

etc!

Each dimension needs a new parameter, and the sum goes 0,2,0,2,...

Perhaps I should mention that?

]]>Likewise if you included another vertex (say

half wayalong a line)

you would get an extra edge, too.

Not really a mistake; Just that halfway, in this sense, would be a single word.

No other mistakes are visible to me on that page. It certainly is very informative and gives the reader a *huge* idea of more on Platonic Solids. Nice work; Yet another document to add to the collection.

EDIT: I must be an advanced topologist, then.

]]>So does that mean that Euler's formula is useless now? F+V-E = something

Or can you define a set of properties so that any solid that meets them will make F+V-E=2 work?

Nice page though. Very interesting, and I couldn't find any mistakes. Although there might be some that can only be spotted by advanced topologists.

]]>I wasn't sure how to approach it, because "F+V-E=2" is often taught, so I thought "OK, let's do that, then show it isn't"

Good strategy? Or does it not flow very well?

And I am not sure if I am on solid ground when I say "that doesn't intersect itself". Convention is to just say "not concave", but a polyhedron can be concave and still have F+V-E=2. Anyone have any better knowledge on this?

]]>Have a read of Platonic Solids - Why Five?, and tell me if it makes sense (and if I made any mistakes )

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