{"title":"Eberhard-type theorems with two kinds of polygons","authors":"Sebastian Manecke","doi":"10.1142/9789811200489_0017","DOIUrl":null,"url":null,"abstract":"Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new theorems of Eberhard-type where we allow adding two kinds of polygons and one type of vertices. We also hint towards a full classification of these types of results.","PeriodicalId":322478,"journal":{"name":"Algebraic and Geometric Combinatorics on Lattice Polytopes","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Combinatorics on Lattice Polytopes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789811200489_0017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new theorems of Eberhard-type where we allow adding two kinds of polygons and one type of vertices. We also hint towards a full classification of these types of results.
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