# A Polyhedral Journey, Beginning With an Expansion of the Rhombic Triacontahedron

The blue figure below is the rhombic triacontahedron. It has thirty identical faces, and is one of the Catalan solids, also known as Archimedean duals. This particular Catalan solid’s dual is the icosidodecahedron.

I use a program called Stella 4d (available here) to transform polyhedra, and the next step here was to augment each face of this polyhedron with a prism, keeping all edge lengths the same.

After that, I created the convex hull of this prism-augmented rhombic triacontahedron, which is the smallest convex figure which can enclose a given polyhedron.

Another ability of Stella is the “try to make faces regular” function. Throwing this function at this four-color polyhedron above produced the altered version below, in which edge lengths are brought as close together as possible. It isn’t possible to do this perfectly, though, and that is most easily seen in the yellow faces. While close to being squares, they are actually trapedoids.

For the next transformation, I looked at the dual of this polyhedron. If I had to name it, I would call it the trikaipentakis icosidodecahedron. It has two face types: sixty of the larger kites, and sixty of the smaller ones, also.

Next, I used prisms, again, to augment each face. The height used for these prisms is the length of the edges where orange kites meet purple kites.

Lastly, I made the convex hull of the polyhedron above. This convex hull appears below.

# Explaining China, Part III: Basic International Etiquette Involving the Chinese, as well as their Korean and Japanese “Neighbors,” and Americans

Multiple East Asian nations are discussed in this post, the third of a series which began here, and is usually focused only on China, and the Han Chinese. Those nations are The People’s Republic of China (the PRC); Taiwan, officially known as the Republic of China (ROC); North Korea; South Korea; and Japan. Many Americans, when they see a person whom they think is from East Asia (based on appearance), will simply guess — and sometimes they go even further, and guess out loud. This is usually not intentional rudeness, but it is a socially-dangerous breach of etiquette, made all the more serious if a spoken guess is an incorrect one. The reasons for this are complex, involving such things as tense relationships between ethnic groups and historical atrocities. The etiquette-based solution to avoid walking into a metaphorical minefield, once understood, is a simple set of principles. If you simply want to look for the principles, and skip the explanation of how I learned these things, and why they make sense, simply look for the red, centered text.

1. Listen carefully, before and after talking.

2. Silence is seldom considered rude.

3. Every interaction (as might happen playing the game above) is an opportunity to learn.

The board and stones above will be recognized, as the game of go, by many people around the world. Go is the national game of Japan. Although I would never say this if I were in Japan, this game originated in China. The Chinese call it weiqi (pronounced “way-chee”), and the Japanese call it igo (this word sounds like the English word “ego”). Japan introduced this game to the Western world, which is why its English name is similar to the Japanese, rather than the Chinese, name. However, I did not learn this game from a Chinese nor a Japanese person, so, when in the presence of this teacher (who taught me taekwondo as well), I had to remember to call the game baduk, its name in Korean.

4. If you must guess about ethnicity, keep your guesses to yourself.

At the time I learned both go and taekwondo, I was a young teenager. The angriest I ever saw this teacher was an occasion where an American adult assumed, out loud, that he was Japanese. Being young, I didn’t put cause and effect together by myself, but it was later explained to me: during World War II, which had ended less than forty years ago at that time, atrocities had been committed by Japanese during World War II in South Korea. My teacher immigrated to the United States from South Korea a generation later, in 1977, and the angriest I ever saw him was in reaction to this blunder by the American who called him Japanese, because of what had happened to his nation during WWII.

There have been many other conflicts between East Asian nations, as well, including China, which was also invaded by Japan. Following WWII (which ended with the USA dropping two atomic bombs on Japanese cities), the Korean War started, which brought China into conflict with both Koreans and the USA. All these conflicts are within living memory, meaning that there are people still alive who remember these things happening. These international conflicts (and earlier ones, of course) are a major reason for inter-ethnic conflict, and few people want to be confused with their historical enemies.

5. An understanding of history can explain much basic etiquette.

Later still, I encountered other ways people can make social blunders of related types. For example, anyone born in the USA is an American citizen, and can be legitimately called an American — and that’s a term to which most American citizens do not object. If the person’s parents came from, say, Taiwan, and they are ethnically of the Han, this creates a situation few Americans understand, for the whole China/Taiwan thing is certainly complex. Under such circumstances, it’s perfectly understandable that one might prefer to be called “American,” rather than having to try to explain exactly which China one’s parents immigrated from. Many Americans, after all, do not even know that two Chinese governments (the PRC’s in Beijing, and the ROC’s in Taipei, both claiming for decades to be the government of all of Greater China) exist.

However, there is an even better way to refer to individual people — any people, anywhere.

6. When possible, use people’s names and/or titles, expressed politely, and pronounced correctly.

With my taekwondo and baduk teacher, for example, it was seldom necessary to call him anything other than “Mr. Lee,” or simply, “sir.” I knew he was Korean, and from South Korea, but that was seldom discussed. I learned much by simply paying attention to him, and he taught me a lot. Later, I learned things about Japan, mostly from exposure to, and conversation with, Japanese people. Still later, I began learning about China (both the PRC and the ROC) and the Han, and found that my best sources of information were — no surprise — people of the Han, themselves.

7. For more detailed advice on etiquette, seek insider sources.

This means that, if you’re preparing to visit mainland China (the PRC), and want advice to avoid social blunders there, you’ll get your best information from those who have lived in the PRC. Similar principles apply to other places, such as my learning elements of Korean etiquette from a Korean. With people who are currently located in the PRC, though, one must carefully stay on topic, and there is one topic which must be avoided.

8. To avoid putting them in danger from their own government, do not discuss political issues with anyone located in the People’s Republic of China.

This would also apply to North Korea (formally: the Democratic People’s Republic of Korea, or DPRK), but that is far less likely to come up, simply because the PRC now encourages foreign tourism there, while the DPRK remains a closed society, as the PRC was during the reign of Chairman Mao. Both of these governments are totalitarian, are perfectly willing to kill their own citizens, and will not tolerate any propaganda (discussing, say, democracy, or human rights, would count as propaganda), except for their own.

Principle #9, below, is essential to understanding anything about these East Asian nations. When I studied East Asian history in graduate school, this was my starting point.

9. China ≠ Japan ≠ Korea.

10. Remember that these are basic principles only, and use #7 to learn more.

It would be a mistake for anyone to take this as a complete list, for it is not.

[Image credit: I found the image of a weiqi/baduk/igo/go set on eBay, right here. It is for sale for the next few weeks.]