{"title":"最短路径的魔方蛇prime节与多达6个交叉点和应用于过山车的设计","authors":"Songming Hou, Jianning Su, Ramon Mufutau","doi":"10.15406/iratj.2023.09.00259","DOIUrl":null,"url":null,"abstract":"A Rubik’s Snake is a toy that was invented over 40 years ago together with the more famous Rubik’s Cube. It can be twisted to many interesting shapes including knots. Four blocks can form a trivial knot. Previously we have studied the shortest paths for Rubik’s Snake prime knots with up to 5 crossings. In this paper we study how many blocks are needed to form prime knots with 6 crossings. There are three different types of such knots. The results are classified using the DT (Dowker-Thistlethwaite) code. We also apply our findings to roller coaster design by using the tube version of the Rubik’s snake.","PeriodicalId":346234,"journal":{"name":"International Robotics & Automation Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Shortest paths of Rubik’s snake prime knots with up to 6 crossings and application to roller coaster design\",\"authors\":\"Songming Hou, Jianning Su, Ramon Mufutau\",\"doi\":\"10.15406/iratj.2023.09.00259\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A Rubik’s Snake is a toy that was invented over 40 years ago together with the more famous Rubik’s Cube. It can be twisted to many interesting shapes including knots. Four blocks can form a trivial knot. Previously we have studied the shortest paths for Rubik’s Snake prime knots with up to 5 crossings. In this paper we study how many blocks are needed to form prime knots with 6 crossings. There are three different types of such knots. The results are classified using the DT (Dowker-Thistlethwaite) code. We also apply our findings to roller coaster design by using the tube version of the Rubik’s snake.\",\"PeriodicalId\":346234,\"journal\":{\"name\":\"International Robotics & Automation Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Robotics & Automation Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15406/iratj.2023.09.00259\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Robotics & Automation Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15406/iratj.2023.09.00259","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Shortest paths of Rubik’s snake prime knots with up to 6 crossings and application to roller coaster design
A Rubik’s Snake is a toy that was invented over 40 years ago together with the more famous Rubik’s Cube. It can be twisted to many interesting shapes including knots. Four blocks can form a trivial knot. Previously we have studied the shortest paths for Rubik’s Snake prime knots with up to 5 crossings. In this paper we study how many blocks are needed to form prime knots with 6 crossings. There are three different types of such knots. The results are classified using the DT (Dowker-Thistlethwaite) code. We also apply our findings to roller coaster design by using the tube version of the Rubik’s snake.
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