Talk:Planigon

Creation
I created this article because there was no clear devoted place for the planigons on existing articles. The tiles exist in the Duals of the k-uniform tilings at Euclidean tilings by convex regular polygons. It may be material should eventually be moved to a second article for these dual k-uniform figures. Images are listed here on a user page User:Tomruen/uniform_tilings. Tom Ruen (talk) 21:06, 13 July 2019 (UTC)

Harry Princeton
Tomruen, thanks for your kind notification :).

I'm sorry I have to say it to you this way, but I will: I'm really not going to argue with you, but it isn't your page at all. I have once again added the additional sections from User:Harry Princeton/Planigons and Dual Uniform Tilings, which you have no right to edit BTW. Also, I have once changed again 'Planigons.png' to '21 Possible Vertex Polygons.png' in Euclidean tilings by convex regular polygons since you have incidentally derived my work from Euclidean tilings by convex regular polygons. Notice I have not reverted/deleted or overwritten your edits, except for your derived work, but acted faithfully. So it is collaboration, however disagreeable to your taste. Thanks!

P.S. You had spelled 'unuseable' wrong. Harry Princeton (talk) 19:52, 15 July 2019 (UTC)

As a further and impersonal note, please kindly see the updated Talk:Euclidean tilings by convex regular polygons. You have inadvertently used my initiative to your advantage. Finally, I personally prefer 'semiplangion' (or at least 'demiplanigon') over 'semiregular/demiregular/hemiregular/etc. planigons'; I know the latter language is well-known (Wolfram, Demiregular tiling, etc.) but it may still be confusing. Also I have written 'semiplanigon' in Euclidean tilings by convex regular polygons, List of Euclidean uniform tilings, and our talk, before you have created Planigon. Moreover, the 'semiplanigons' are not specific to Demiregular tilings, but instead only need at least one accompanying planigon. i.e. The skew quadrilateral V3.3.4.12 'needs' the regular hexagon; the tie kite V3.4.3.12 'needs' the isosceles obtuse triangle; the isosceles trapezoid V3.3.6.6 'needs' the rhombus; the right trapezoid V3.4.4.6 'needs' the rhombus; for 2-dual-uniform fillings (minimal k possible for them to exist), but higher dual uniform fillings use them as well. Harry Princeton (talk) 21:11, 15 July 2019 (UTC)

Terminology
On terminology we shouldn't clearly go on personal preferences, but existing usage. Myself, I'm not sure what names should be used, while planigon seemed a nice name to go with for the tiles itself. What sources do you consider definitive for terminology? Tom Ruen (talk) 22:23, 15 July 2019 (UTC)

Can you read Russian? But just glancing here, I think planigons are more general than these most symmetric forms. And I'm guessing the demi-forms (requiring 2+ tiles) don't count at all. It looks more like monohedral tiling. Tom Ruen (talk) 22:28, 15 July 2019 (UTC)


 * Perhaps Laves tilings is a better title for this k-uniform dual content? What sources do we have on k-uniform duals, even 2-uniform duals? Tom Ruen (talk) 22:40, 15 July 2019 (UTC)

Thanks for your kind consideration on my contributions. I left it at demiplanigons. Harry Princeton (talk) 23:30, 15 July 2019 (UTC)


 * Are semiplanigon or demiplanigon used anywhere outside your imagination? Tom Ruen (talk) 02:58, 16 July 2019 (UTC)

P.S. Did you color your planigons orange because orange is Princeton University's color?

If you could actually do mirror images (mere reflections), this would be great. Like 3.3.4.12 → 12.4.3.3. Thanks! Harry Princeton (talk) 03:05, 16 July 2019 (UTC)


 * I'm still thinking probably this is still insane, and this article should be about defining planigons and not listed duals to k-uniforms. I've yet to see an actual definition and sources seem to be in Russian.
 * Also this graphic is crazy large, doesn't belong in an article, at best should be multiple images with actual text in Wikipedia. No Wikipedia page has poster-size images like you're making. Tom Ruen (talk) 01:01, 17 July 2019 (UTC)
 * I don't think demiregular planigons EXIST, unless you have sources to defend it. Tom Ruen (talk) 01:03, 17 July 2019 (UTC)
 * The most basic opening sentence contradicts most of what is being shown here "a planigon is a polygon that can fill the plane with only copies of itself." We might have an article called Euclidean tilings with planigons, but that would still exclude tiles that don't tile the plane by itself. Tom Ruen (talk) 01:46, 17 July 2019 (UTC)

That is exactly what I thought. Based on the original definition of 'planigon,' all triangles and all quadrilaterals are planigons. Or just simple tesselations. Conversely, this page should be named Duals to Euclidean Uniform Convex Tilings or Euclidean tilings of regular vertex polygons. Also, I am not surprised that you don't like my large image, but life's life. Unless, of course, you want to delete this page. Harry Princeton (talk) 02:49, 17 July 2019 (UTC)

Gruenbaum and Shephard identify "Tilings with regular vertices" which include other solutions. So this article probably should focus on actual Lave tilings and variations.

Prismatic pentagonal tiling also has distorted forms. Tom Ruen (talk) 05:28, 17 July 2019 (UTC)

Planigon vs. plangion
Both these words are used at several places in the article as well as on the talk-page. Unfortunately, I can not find out whether one of these words is a misspelling of the other or if they mean two different things. Could any of you clarify? Thanks! 130.239.42.221 (talk) 16:56, 15 October 2023 (UTC)

Minor errors in the table 'Regular Polygons and Planigons'
I believe there are two minor errors in the table that lists the side lengths and areas of the different planigons.

Have I made an error while calculating this? Eisenstein Integer (talk) 12:21, 30 April 2024 (UTC)
 * For the 4.8.8 planigon (i), the length of the hypotenuse is listed as having the length ½ + 1/√2, but if one uses the pythagorean theorem, knowing the other sides both have the length 1 + 1/√2, results in 1 + √2, and if one adds the apothem of an octagon to the apothem of the other octagon one adds ½*(1+√2) to ½*(1+√2), which is also clearly 1+√2, not ½ + 1/√2
 * For the 4.6.12 planigon (3), the area is given as ¾ + 3√3/2, but if one adds a quarter of the area of a square (¼) to a sixth of the area of a hexagon (√3/4) to a twelfth of the area of a dodecagon ((2+√3)/4) one gets ¾ + 2√3/4 = ¾ + √3/2, not ¾ + 3√3/4, and if one uses the perpendicular sides to calculate it one gets (1+√3)/2 * (3+√3)/2 * ½, which is also ¼*(3+2√3) = ¾+√3/2


 * I realise this is not very clear, but wherever is written √a/b, it is meant as √(a)/b and not √(a/b) Eisenstein Integer (talk) 12:23, 30 April 2024 (UTC)