{"title":"教学经验。XIV.关于四面体的多样性","authors":"Yuriy Voytehovskiy","doi":"10.19110/geov.2024.4.4","DOIUrl":null,"url":null,"abstract":"The paper proposes the derivation of 25 combinatorial-geometric kinds of tetrahedrons belonging to 8 point symmetry groups. Among them are 3 simple forms: cubic (-43m), tetragonal (-42m) and rhombic (222) tetrahedrons; and 5 combinations: trigonal pyramid and monohedron (3m), 2 planar dihedrons (mm2, 2 kinds), 2 axial dihedrons (2, 3 kinds), planar dihedron and 2 monohedrons (m, 5 kinds), 4 monohedrons (1, 11 kinds). It is shown that tetrahedrons with symmetry 23, -4 and 3 — subgroups of the point symmetry group of the cubic tetrahedron — are impossible. The example is recommended for consideration in the course of crystallography on «simple forms and their combinations».","PeriodicalId":23572,"journal":{"name":"Vestnik of geosciences","volume":"25 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"From teaching experience. XIV. On the variety of tetrahedrons\",\"authors\":\"Yuriy Voytehovskiy\",\"doi\":\"10.19110/geov.2024.4.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper proposes the derivation of 25 combinatorial-geometric kinds of tetrahedrons belonging to 8 point symmetry groups. Among them are 3 simple forms: cubic (-43m), tetragonal (-42m) and rhombic (222) tetrahedrons; and 5 combinations: trigonal pyramid and monohedron (3m), 2 planar dihedrons (mm2, 2 kinds), 2 axial dihedrons (2, 3 kinds), planar dihedron and 2 monohedrons (m, 5 kinds), 4 monohedrons (1, 11 kinds). It is shown that tetrahedrons with symmetry 23, -4 and 3 — subgroups of the point symmetry group of the cubic tetrahedron — are impossible. The example is recommended for consideration in the course of crystallography on «simple forms and their combinations».\",\"PeriodicalId\":23572,\"journal\":{\"name\":\"Vestnik of geosciences\",\"volume\":\"25 4\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik of geosciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19110/geov.2024.4.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik of geosciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19110/geov.2024.4.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
From teaching experience. XIV. On the variety of tetrahedrons
The paper proposes the derivation of 25 combinatorial-geometric kinds of tetrahedrons belonging to 8 point symmetry groups. Among them are 3 simple forms: cubic (-43m), tetragonal (-42m) and rhombic (222) tetrahedrons; and 5 combinations: trigonal pyramid and monohedron (3m), 2 planar dihedrons (mm2, 2 kinds), 2 axial dihedrons (2, 3 kinds), planar dihedron and 2 monohedrons (m, 5 kinds), 4 monohedrons (1, 11 kinds). It is shown that tetrahedrons with symmetry 23, -4 and 3 — subgroups of the point symmetry group of the cubic tetrahedron — are impossible. The example is recommended for consideration in the course of crystallography on «simple forms and their combinations».