Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes

We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of geometry 2019-12, Vol.110 (3), p.1-12, Article 47
Hauptverfasser:	Itoh, Jin-ichi, Nara, Chie
Format:	Artikel
Sprache:	eng
Schlagworte:	Geometry Mathematics Mathematics and Statistics Polytopes Tetrahedra
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	12
container_issue	3
container_start_page	1
container_title	Journal of geometry
container_volume	110
creator	Itoh, Jin-ichi Nara, Chie
description	We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to higher dimensional regular simplexes and cross-polytopes by considering the 2-dimensional skeleton of a polytope corresponding to the surface of a three dimensional polyhedron.
doi_str_mv	10.1007/s00022-019-0504-0
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2284676719</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2284676719</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-af1f2441884e260f73e73caa4af1c9db07ece37fb0a8a8ca050410db67b73cd03</originalsourceid><addsrcrecordid>eNp1kEFLxDAQhYMouK7-AG8Bz9FJGpv2KIu6woIIeg5pO1m7dpOapOD-e1srePI0h_neezOPkEsO1xxA3UQAEIIBLxncgmRwRBZcCmBFWapjsgCQigmZF6fkLMbdSGciLxfkZeVdat3gh0htZ1JC17ot9Zamd6SCxQ_sMHkXaetowO3QmUBju-87_MJIjWtoHXyMrPfdIfke4zk5saaLePE7l-Tt4f51tWab58en1d2G1RnPEzOWWyElLwqJIgerMlRZbYwcF3XZVKCwxkzZCkxhitpMX3FoqlxVI9dAtiRXs28f_OeAMemdH4IbI7UQhcxVrng5Unymfq4MaHUf2r0JB81BT83puTk9NqenDD05i1kTR9ZtMfw5_y_6Bl1Vcbo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2284676719</pqid></control><display><type>article</type><title>Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes</title><source>SpringerLink Journals</source><creator>Itoh, Jin-ichi ; Nara, Chie</creator><creatorcontrib>Itoh, Jin-ichi ; Nara, Chie</creatorcontrib><description>We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to higher dimensional regular simplexes and cross-polytopes by considering the 2-dimensional skeleton of a polytope corresponding to the surface of a three dimensional polyhedron.</description><identifier>ISSN: 0047-2468</identifier><identifier>EISSN: 1420-8997</identifier><identifier>DOI: 10.1007/s00022-019-0504-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Geometry ; Mathematics ; Mathematics and Statistics ; Polytopes ; Tetrahedra</subject><ispartof>Journal of geometry, 2019-12, Vol.110 (3), p.1-12, Article 47</ispartof><rights>Springer Nature Switzerland AG 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-af1f2441884e260f73e73caa4af1c9db07ece37fb0a8a8ca050410db67b73cd03</citedby><cites>FETCH-LOGICAL-c316t-af1f2441884e260f73e73caa4af1c9db07ece37fb0a8a8ca050410db67b73cd03</cites><orcidid>0000-0003-0748-9200</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00022-019-0504-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00022-019-0504-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Itoh, Jin-ichi</creatorcontrib><creatorcontrib>Nara, Chie</creatorcontrib><title>Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes</title><title>Journal of geometry</title><addtitle>J. Geom</addtitle><description>We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to higher dimensional regular simplexes and cross-polytopes by considering the 2-dimensional skeleton of a polytope corresponding to the surface of a three dimensional polyhedron.</description><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polytopes</subject><subject>Tetrahedra</subject><issn>0047-2468</issn><issn>1420-8997</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLxDAQhYMouK7-AG8Bz9FJGpv2KIu6woIIeg5pO1m7dpOapOD-e1srePI0h_neezOPkEsO1xxA3UQAEIIBLxncgmRwRBZcCmBFWapjsgCQigmZF6fkLMbdSGciLxfkZeVdat3gh0htZ1JC17ot9Zamd6SCxQ_sMHkXaetowO3QmUBju-87_MJIjWtoHXyMrPfdIfke4zk5saaLePE7l-Tt4f51tWab58en1d2G1RnPEzOWWyElLwqJIgerMlRZbYwcF3XZVKCwxkzZCkxhitpMX3FoqlxVI9dAtiRXs28f_OeAMemdH4IbI7UQhcxVrng5Unymfq4MaHUf2r0JB81BT83puTk9NqenDD05i1kTR9ZtMfw5_y_6Bl1Vcbo</recordid><startdate>20191201</startdate><enddate>20191201</enddate><creator>Itoh, Jin-ichi</creator><creator>Nara, Chie</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-0748-9200</orcidid></search><sort><creationdate>20191201</creationdate><title>Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes</title><author>Itoh, Jin-ichi ; Nara, Chie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-af1f2441884e260f73e73caa4af1c9db07ece37fb0a8a8ca050410db67b73cd03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polytopes</topic><topic>Tetrahedra</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Itoh, Jin-ichi</creatorcontrib><creatorcontrib>Nara, Chie</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Itoh, Jin-ichi</au><au>Nara, Chie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes</atitle><jtitle>Journal of geometry</jtitle><stitle>J. Geom</stitle><date>2019-12-01</date><risdate>2019</risdate><volume>110</volume><issue>3</issue><spage>1</spage><epage>12</epage><pages>1-12</pages><artnum>47</artnum><issn>0047-2468</issn><eissn>1420-8997</eissn><abstract>We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to higher dimensional regular simplexes and cross-polytopes by considering the 2-dimensional skeleton of a polytope corresponding to the surface of a three dimensional polyhedron.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00022-019-0504-0</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0003-0748-9200</orcidid></addata></record>
fulltext	fulltext
identifier	ISSN: 0047-2468
ispartof	Journal of geometry, 2019-12, Vol.110 (3), p.1-12, Article 47
issn	0047-2468 1420-8997
language	eng
recordid	cdi_proquest_journals_2284676719
source	SpringerLink Journals
subjects	Geometry Mathematics Mathematics and Statistics Polytopes Tetrahedra
title	Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-24T19%3A29%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Continuous%20flattening%20of%20the%202-skeletons%20in%20regular%20simplexes%20and%20cross-polytopes&rft.jtitle=Journal%20of%20geometry&rft.au=Itoh,%20Jin-ichi&rft.date=2019-12-01&rft.volume=110&rft.issue=3&rft.spage=1&rft.epage=12&rft.pages=1-12&rft.artnum=47&rft.issn=0047-2468&rft.eissn=1420-8997&rft_id=info:doi/10.1007/s00022-019-0504-0&rft_dat=%3Cproquest_cross%3E2284676719%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2284676719&rft_id=info:pmid/&rfr_iscdi=true