Cubic Tessellations of the Helicosms
Up to isomorphism, there are six fixed-point free crystallographic groups in Euclidean 3-space E 3 generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E 3 by such a group. The cubic tessellation of E 3 induces tessellations on each such manifold...
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| Veröffentlicht in: | Discrete & computational geometry 2015-10, Vol.54 (3), p.686-704 |
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| creator | Hubard, Isabel Mixer, Mark Pellicer, Daniel Weiss, Asia Ivić |
| description | Up to isomorphism, there are six fixed-point free crystallographic groups in Euclidean 3-space
E
3
generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of
E
3
by such a group. The cubic tessellation of
E
3
induces tessellations on each such manifold. The corresponding classification for the 3-torus and the didicosm were classified as ‘equivelar toroids’ and ‘cubic tessellation of the didicosm’ in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds. |
| doi_str_mv | 10.1007/s00454-015-9721-y |
| format | Article |
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E
3
generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of
E
3
by such a group. The cubic tessellation of
E
3
induces tessellations on each such manifold. The corresponding classification for the 3-torus and the didicosm were classified as ‘equivelar toroids’ and ‘cubic tessellation of the didicosm’ in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-015-9721-y</identifier><identifier>CODEN: DCGEER</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Classification ; Combinatorics ; Computational geometry ; Computational Mathematics and Numerical Analysis ; Crystallography ; Euclidean geometry ; Manifolds ; Mathematics ; Mathematics and Statistics ; Screws ; Tessellation ; Texts</subject><ispartof>Discrete & computational geometry, 2015-10, Vol.54 (3), p.686-704</ispartof><rights>Springer Science+Business Media New York 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c419t-10ebc628944ea839c7a8cb88451ea4fff04a70b42f81e6daaa8620a4586aefa43</citedby><cites>FETCH-LOGICAL-c419t-10ebc628944ea839c7a8cb88451ea4fff04a70b42f81e6daaa8620a4586aefa43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00454-015-9721-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-015-9721-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Hubard, Isabel</creatorcontrib><creatorcontrib>Mixer, Mark</creatorcontrib><creatorcontrib>Pellicer, Daniel</creatorcontrib><creatorcontrib>Weiss, Asia Ivić</creatorcontrib><title>Cubic Tessellations of the Helicosms</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>Up to isomorphism, there are six fixed-point free crystallographic groups in Euclidean 3-space
E
3
generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of
E
3
by such a group. The cubic tessellation of
E
3
induces tessellations on each such manifold. The corresponding classification for the 3-torus and the didicosm were classified as ‘equivelar toroids’ and ‘cubic tessellation of the didicosm’ in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds.</description><subject>Classification</subject><subject>Combinatorics</subject><subject>Computational geometry</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Crystallography</subject><subject>Euclidean geometry</subject><subject>Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Screws</subject><subject>Tessellation</subject><subject>Texts</subject><issn>0179-5376</issn><issn>1432-0444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp10DFPwzAQBWALgUQp_AC2SDCwGO6Sc-KMqKIUqRJLmS3H2JAqTUouGfrvcRUGhMR0y_eeTk-Ia4R7BCgeGIAUSUAlyyJFeTgRM6QslUBEp2IGWJRSZUV-Li6YtxB5CXombhdjVbtk45l909ih7lpOupAMnz5Z-aZ2He_4UpwF27C_-rlz8bZ82ixWcv36_LJ4XEtHWA4SwVcuT3VJ5K3OSldY7SqtSaG3FEIAsgVUlAaNPn-31uo8BUtK59YHS9lc3E29-777Gj0PZlezO_7V-m5kg4XKFMb-PNKbP3TbjX0bv4sKylRhlFHhpFzfMfc-mH1f72x_MAjmuJuZdjNxN3PczRxiJp0yHG374ftfzf-GvgGrv27L</recordid><startdate>20151001</startdate><enddate>20151001</enddate><creator>Hubard, Isabel</creator><creator>Mixer, Mark</creator><creator>Pellicer, Daniel</creator><creator>Weiss, Asia Ivić</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20151001</creationdate><title>Cubic Tessellations of the Helicosms</title><author>Hubard, Isabel ; 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E
3
generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of
E
3
by such a group. The cubic tessellation of
E
3
induces tessellations on each such manifold. The corresponding classification for the 3-torus and the didicosm were classified as ‘equivelar toroids’ and ‘cubic tessellation of the didicosm’ in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00454-015-9721-y</doi><tpages>19</tpages></addata></record> |
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| subjects | Classification Combinatorics Computational geometry Computational Mathematics and Numerical Analysis Crystallography Euclidean geometry Manifolds Mathematics Mathematics and Statistics Screws Tessellation Texts |
| title | Cubic Tessellations of the Helicosms |
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