What is a quick summary of Chapter VI of The Twenty-One Balloons by William Pene du Bois?

Chapter VI of The Twenty-One Balloons (Dubois), is entitled "The Gourmet Government."  In this chapter, Professor Sherman wakes up in comfort in a canopied bed in a beautifully furnished room in the home of the F family. As he and Mr. F. leave the house to go to breakfast, he notices that everything in the house inside and outside is French.  He observes other homes with national "themes," for example, one American, one British, one Chinese, and one Dutch.  Mr F. and Professor Sherman enter the British house, where Mr. F. introduces him to the dozens of people who are also there for breakfast.  Professor Sherman is greeted and applauded, and while breakfast proceeds, Mr. F. tells the story of how all of these people came to be on a volcanic island filled with diamonds. 
Eight years previously, a shipwrecked sailor, now known as Mr. M., landed on Krakatoa, and trying to stay away from the mountainous area, once he realized it held an active volcano, stumbled into the jungle and serendipitously came upon the diamond mines.  He thought carefully about how he could best capitalize on this find, built himself a raft, and managed to get himself to San Francisco with some diamonds, which he sold, carefully, so that there would be not too much interest in him and so that he would not destroy the value of the diamonds by flooding the market. He then selected twenty families, each with one young son and one young daughter, people who had exhibited creativity in their lives in areas such as the arts or the sciences. He persuaded them to join him on Krakatoa, with the lure of wealth and an island paradise they could create together.  Arriving at Krakatoa, there was a fairly steep learning curve for the families, who were overwhelmed by the diamonds and not exactly ready to live happily and cooperatively together in a Utopia.  Ultimately, though, all of the new residents came to understand that cooperation would be better than competition.  This eventually led to what they called "A Restaurant Government" (Dubois 87).
Each family chose a nationality-themed restaurant, and along with the restaurant, each family's home and identity was nationality-based.  The family names became the first initial of the nationality, so that the A family was American, the B family was British, and so on. This explained why the F family's home was all French.  Each family prepared meals for all the other families for a day, rotating through all of the families and then beginning anew. This led to a revised calendar of twenty days for each month, and eighteen months in the Krakatoan year.  In order to raise money to purchase the materials and supplies needed for all the families on the island, the Krakatoans scoop up a few diamonds from time to time, take them to another place, sell them, fill up a freighter with what is needed and bring it all back to the island.
Professor Sherman is unsure of his status in this situation, not being part of a family, not having a house, not having any stake in the diamond mines.  Mr. F. explains that he can be a "perpetual guest" (91), who is welcome to stay with the F. family or move around. He will simply join in on the meals each day, wherever they may be.  Mr. F. also makes a joke about Professor Sherman not wanting the next letter of the alphabet for a new name, since it is "U."  If people called for him, no one would ever know if they meant "U" or "you."