{"title":"An open problem on metric invariants of tetrahedra","authors":"Lu Yang, Zhenbing Zeng","doi":"10.1145/1073884.1073934","DOIUrl":null,"url":null,"abstract":"In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for any given positive real constants V,R,A1,A2,A3,A4, there are always finitely many tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T(x,y) where $(x,y)$ varies over a component of a cubic curve such that all tetrahedra T(x,y) share the same volume, circumradius and face areas.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1073884.1073934","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for any given positive real constants V,R,A1,A2,A3,A4, there are always finitely many tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T(x,y) where $(x,y)$ varies over a component of a cubic curve such that all tetrahedra T(x,y) share the same volume, circumradius and face areas.
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