# Complex inversions **URL:** \ **Category:** Factual Questions\ **Created:** [May 28, 2021, 9:33am UTC](https://boards.straightdope.com/t/complex-inversions/943078 "2021-05-28T09:33:55Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 9:33am UTC](https://boards.straightdope.com/t/complex-inversions/943078/1 "2021-05-28T09:33:55Z")
I’m looking for instances of complex inversions of design elements. To give you an idea of what I mean, here’s a few examples: > **[Flag of Cuba](https://en.wikipedia.org/wiki/Flag_of_Cuba)** > > Pages for logged out editors learn more > > The national flag of Cuba (Spanish: Bandera de Cuba) consists of five alternating stripes (three blue and two white) and a red equilateral triangle at the hoist, within which is a white five-pointed star. It was designed in 1849 and officially adopted May 20, 1902. The flag is referred to as the Estrella Solitariacode: spa promoted to code: es , or the Lone Star flag. It is in the stars and stripes flag family. > Fighting against the Spanish Crown ... > **[Flag of Puerto Rico](https://en.wikipedia.org/wiki/Flag_of_Puerto_Rico)** > > Pages for logged out editors learn more > > > The flag of Puerto Rico (Spanish: Bandera de Puerto Rico) represents and symbolizes Puerto Rico and its people. > The origins of the current flag of Puerto Rico, adopted by the Commonwealth of Puerto Rico in 1952, can be traced to 1868, when the first Puerto Rican flag, "The Revolutionary Flag of Lares", was conceived by Dr. Ramón Emeterio Betances and embroidered by Mariana "Brazos de Oro" Bracetti. This flag was used in the short-lived Puerto R... The colors red and blue are inverted between the flags of Cuba and Puerto Rico. This was deliberate on the part of Puerto Rican revolutionaries who modified the Cuban revolutionary flag to come up with their flag. Another inversion, this one not intentional, is those of Norway and Iceland: > **[Flag of Norway](https://en.wikipedia.org/wiki/Flag_of_Norway)** > > Pages for logged out editors learn more > > > The national flag of Norway (Bokmål: Norges flagg; Nynorsk: Noregs flagg; lit. 'Norway's flag') is red with a navy blue Scandinavian cross fimbriated in white that extends to the edges of the flag; the vertical part of the cross is shifted to the hoist side in the style of the Dannebrog, the flag of Denmark. > It is difficult to establish what the earliest flag of Norway looked like. During ancient times countries did not fly flags. Kings and oth... > **[Flag of Iceland](https://en.wikipedia.org/wiki/Flag_of_Iceland)** > > Pages for logged out editors learn more > > The flag of Iceland (Icelandic: íslenski fáninn) was officially described in Law No. 34, set out on 17 June 1944, the day Iceland became a republic. The law is entitled "The Law of the National Flag of Icelanders and the State Arms" and describes the Icelandic flag as follows: > The civil national flag of Icelanders is blue as the sky with a snow-white cross, and a fiery-red cross inside the white cross. The arms of the cross extend to the edge of ... The exact shades of blue are different, but in the past, the blue on Iceland’s flag used to be darker. Note that these inversions are a bit more complex than a simple swapping of two stripes of a tricolor or bicolor. There are some of those out there, but I’m not interest in them. Another example of complex inversion is the vowels in the words **cacao** and **cocoa**. Cacao is a plant, cocoa is the product of that plant. This was also not deliberate, but a result of confusion under the influence of the word _coco_, a different tropical plant. Note that this is a more complex inversion than just swapping two letters. There are hundreds, if not thousands, of pairs of words that just a letter swap away from each other. But I’m not interested in those, or at least not for this thread. Also note this question is not restricted to just flags and words. If there’s some other complex inversion, feel free to contribute it. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [May 28, 2021, 9:40am UTC](https://boards.straightdope.com/t/complex-inversions/943078/2 "2021-05-28T09:40:29Z")
I’m still not clear what you mean by “complex” inversion. Why would two colors being swapped in a cross pattern count as complex but not if they are in stripes? What’s the criteria for two words counting as a complex inversion? ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 9:43am UTC](https://boards.straightdope.com/t/complex-inversions/943078/3 "2021-05-28T09:43:47Z")
> [@Mijin](#): > > I’m still not clear what you mean by “complex” inversion. > Why would two colors being swapped in a cross pattern count as complex but not if they are in stripes? Because stripes are the about simplest design element around. > [@](#): > > What’s the criteria for two words counting as a complex inversion? Anything involving more than two letters. Also, it’d be best if there are some letters in common between the two words that are unchanged from one to the other. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [May 28, 2021, 12:46pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/4 "2021-05-28T12:46:49Z")
How about the Swiss flag and the Red Cross flag? > **[Flag of Switzerland](https://en.wikipedia.org/wiki/Flag_of_Switzerland)** > > Pages for logged out editors learn more > > > > The national flag of Switzerland (German: Schweizerfahne; French: drapeau de la Suisse; Italian: bandiera svizzera; Romansh: bandiera da la Svizra) displays a white cross in the centre of a square red field. The white cross is known as the Swiss cross or the federal cross. Its arms are equilateral, and their ratio of length to width is 7:6. The size of the cross in relation to the field was set in 2017 as 5:8. > The white cross has been used as ... > **[Red Cross Flag](https://flagsexpress.com/red-cross-flag/?sku=033408&gclid=EAIaIQobChMIlbeUoLTs8AIVS8DICh2MOQqGEAQYAiABEgJ2bvD_BwE)** > > American Flags Express sells the highest quality Red Cross flags. They are 100% Made in the USA. Give us a call. We'd love to help. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [May 28, 2021, 1:35pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/5 "2021-05-28T13:35:33Z")
> [@dtilque](#): > > Because stripes are the about simplest design element around. OK, but given that there are probably not many flag inversions anyway, you may as well collect them all and ignore the ones that you don’t like. > [@dtilque](#): > > Anything involving more than two letters. Also, it’d be best if there are some letters in common between the two words that are unchanged from one to the other. So swapping only vowels, and at least 3? I think with that requirement, there are relatively few examples. From [this PDF](https://core.ac.uk/download/pdf/62415623.pdf) the best one was RAPIER and REPAIR, many of the others involve uncommon words. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 2:23pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/6 "2021-05-28T14:23:01Z")
> [@Mijin](#): > > OK, but given that there are probably not many flag inversions anyway, you may as well collect them all and ignore the ones that you don’t like. They don’t have to be just national flags, or even flags at all. It could be other graphic images. > [@](#): > > > [@dtilque](#): > > > > Anything involving more than two letters. Also, it’d be best if there are some letters in common between the two words that are unchanged from one to the other. > > So swapping only vowels, and at least 3? I think with that requirement, there are relatively few examples. From [this PDF](https://core.ac.uk/download/pdf/62415623.pdf) the best one was RAPIER and REPAIR, many of the others involve uncommon words. I said letters, not vowels. And those are not what I’m looking for anyway. In the example I gave, cacao/cocoa, all the As are swapped with all the Os. ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [May 28, 2021, 2:24pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/7 "2021-05-28T14:24:30Z")
Flags of Palestine: > **[Flag of Palestine](https://en.wikipedia.org/wiki/Flag_of_Palestine)** > > Pages for logged out editors learn more > > > > The flag of Palestine (Arabic: علم فلسطين) is a tricolor of three equal horizontal stripes (black, white, and green from top to bottom) overlaid by a red triangle issuing from the hoist. This flag is derived from the Pan-Arab colors and is used to represent the State of Palestine and the Palestinian people. It was first adopted on 28 May 1964 by the Palestinian Liberation Organization. The flag day is celebrated on 30 September. > The flag is al... and Sudan: > **[Flag of Sudan](https://en.wikipedia.org/wiki/Flag_of_Sudan)** > > Pages for logged out editors learn more > > > The current flag of Sudan (Arabic: علم السودان, romanized: ʿalam as-Sūdān) was adopted on 20 May 1970 and consists of a horizontal red-white-black tricolour with a green triangle at the hoist. The flag is based on the Arab Liberation Flag of the Egyptian Revolution of 1952, as are the flags of Egypt, Iraq, Syria, Yemen, and Palestine and formerly of the United Arab Republic, North Yemen, South Yemen, and the Libyan Arab Republic. > Whereas there ... And an honourable mention for Kuwait: > **[Flag of Kuwait](https://en.wikipedia.org/wiki/Flag_of_Kuwait)** > > Pages for logged out editors learn more > > > The flag of Kuwait (Arabic: علم الكويت) was adopted on September 7, 1961, and officially hoisted November 24, 1961. Before 1961, the flag of Kuwait was red and white, like those of other Persian Gulf states at the time, with the field being red and words or charges being written in white. > When The Utub settled in Kuwait, Kuwaiti ships were flying a flag common on the western coast of the Persian Gulf, a red flag added to it near the mast a ser... ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 2:34pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/8 "2021-05-28T14:34:33Z")
Actually, those three (Palestine, Sudan, and Kuwait) make up a three-way inversion, or rather rotation. Well except for the truncated triangle, of course. The colors are not swapped, but rather rotated among three locations. The top color moves to the bottom, the bottom color to the triangle, and the triangle color to the top. I was wondering if something like that could be out there. ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [May 28, 2021, 2:36pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/9 "2021-05-28T14:36:02Z")
These two also have some kind of rotation going on: > **[Flag of Cameroon](https://en.wikipedia.org/wiki/Flag_of_Cameroon)** > > Pages for logged out editors learn more > > The national flag of Cameroon (French: drapeau du Cameroun) was adopted in its present form on 20 May 1975 after Cameroon became a unitary state. It is a vertical tricolour of green, red and yellow, with a five-pointed star in its center. There is a wide variation in the size of the central star, although it is always contained within the inside stripe. > The colour scheme uses the traditional Pan-African colours (Cameroon was the second state to a... > **[Flag of Senegal](https://en.wikipedia.org/wiki/Flag_of_Senegal)** > > Pages for logged out editors learn more > > The flag of Senegal (French: drapeau du Sénégal) is a tricolour consisting of three vertical green, yellow and red bands charged with a five-pointed green star at the centre. Adopted in 1960 to replace the flag of the Mali Federation, it has been the flag of the Republic of Senegal since the country gained independence that year. The present and previous flags were inspired by French Tricolour, which flew over Senegal until 1960. > Under French col... ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [May 28, 2021, 2:37pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/10 "2021-05-28T14:37:12Z")
Ghana didn’t quite get with the program: > **[Flag of Ghana](https://en.wikipedia.org/wiki/Flag_of_Ghana)** > > Pages for logged out editors learn more > > The national flag of Ghana consists of a horizontal triband of red, gold, and green. It was designed in replacement of the British Gold Coast's Blue Ensign. > The flag was adopted upon the independence of the Dominion of Ghana on March 6, 1957. It was designed the same year by Theodosia Okoh, a renowned Ghanaian artist. The flag was flown until 1964 and it was then reinstated in 1966. The flag of Ghana consists of the Ethiopian Pan-African colours ... ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 2:40pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/11 "2021-05-28T14:40:34Z")
If the star in the Senegal flag were red, it’d be a simple swap of the red and yellow with Camaroon. So those are almost an inversion. ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [May 28, 2021, 2:45pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/12 "2021-05-28T14:45:57Z")
> [@dtilque](#): > > I said letters, not vowels. And those are not what I’m looking for anyway. In the example I gave, cacao/cocoa, all the As are swapped with all the Os. Do patter and tapper fit your criteria? ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 28, 2021, 2:49pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/13 "2021-05-28T14:49:17Z")
> [@DemonTree](#): > > Do patter and tapper fit your criteria? Certainly do. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [May 28, 2021, 2:54pm UTC](https://boards.straightdope.com/t/complex-inversions/943078/14 "2021-05-28T14:54:43Z")
Re: OP You may be interested in bitmaps that rely on palette-swapping. You can even do animations. > **[Old School Color Cycling with HTML5 | EffectGames.com](http://www.effectgames.com/effect/article-Old_School_Color_Cycling_with_HTML5.html)** > > Anyone remember Color cycling from the 90s? This was a technology often used in 8-bit video games of the era, to achieve interesting visual effects by cycling (shifting) the color palette. Back then video cards could only render 256 colors at a... ~Max ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [May 30, 2021, 2:13am UTC](https://boards.straightdope.com/t/complex-inversions/943078/15 "2021-05-30T02:13:55Z")
In the vocabulary department, I nominate neoplasm and pleonasm. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 30, 2021, 2:30am UTC](https://boards.straightdope.com/t/complex-inversions/943078/16 "2021-05-30T02:30:15Z")
Every polyhedron has what’s called a [dual](https://en.wikipedia.org/wiki/Dual_polyhedron). The dual is what you get when you swap the faces with the vertices. For instance, the dual of the cube is the octahedron. A cube has 6 faces and 8 vertices; an octahedron has 8 faces and 6 vertices. The two are true inverses; if the dual of X is Y, then the dual of Y is X. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 30, 2021, 2:42am UTC](https://boards.straightdope.com/t/complex-inversions/943078/17 "2021-05-30T02:42:55Z")
> [@Senegoid](#): > > In the vocabulary department, I nominate neoplasm and pleonasm. Not quite what I’m looking for, but close. _Atoll_ and _allot_ are the same transposition. As for polyhedrons, IIRC, a tetrahedron is its own dual and icosahedron is the dual of the dodecahdron. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 30, 2021, 2:53am UTC](https://boards.straightdope.com/t/complex-inversions/943078/18 "2021-05-30T02:53:45Z")
> [@dtilque](#): > > As for polyhedrons, IIRC, a tetrahedron is its own dual and icosahedron is the dual of the dodecahdron. That’s right. There are many other “duals” in mathematics, but polyhedra are perhaps the most concrete example. But they mostly arise because graphs (in math, a graph is a collection of points and connections between them) also always have a dual, and many things can be described in some way as a graph. Another example is in electronic circuits, where you can always make a dual circuit where voltage and current are swapped. Swapping again gets you the original circuit. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [May 30, 2021, 2:54am UTC](https://boards.straightdope.com/t/complex-inversions/943078/19 "2021-05-30T02:54:23Z")
Complex inversions you want? Here you go: > **[Inversive geometry](https://en.wikipedia.org/wiki/Inversive_geometry)** > > In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied. Inversion seems to have been discovered by a number of people contemporaneously, including Steiner (1824), Quetelet (1825), Bellavitis (1836), Stubbs and Ingram (1842-3) and Kelvin (1845). > The concept... More at: [http://www.atractor.pt/mat/inversao/inv-C-\_en.html](http://www.atractor.pt/mat/inversao/inv-C-_en.html) : > [@](#): > > By remembering some elementary properties of complex numbers, we can easily give an alternative description of geometric inversion defined previously and deduce some of the listed properties.