{"id":3114,"date":"2012-07-30T19:31:39","date_gmt":"2012-07-31T03:31:39","guid":{"rendered":"http:\/\/bendwavy.org\/wp\/?p=3114"},"modified":"2018-02-24T17:46:55","modified_gmt":"2018-02-25T01:46:55","slug":"soap-films-in-curved-space","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=3114","title":{"rendered":"soap films in curved space"},"content":{"rendered":"<p>A few of the many <a href=\"http:\/\/www.susqu.edu\/brakke\/evolver\/examples\/periodic\/periodic.html\">triply periodic minimal surfaces<\/a> can be generated from a quadrilateral slice through a tetrahedron of mirrors, as refined by Surface Evolver.  I had the idea that the same concept, applied to one of the analogous tetrahedra that tile spherical 3-space, could result in a pretty model.<\/p>\n<p>To my disappointment, none of the non-prismatic kaleidoscopes &#8212; those that generate the six regular polychora &#8212; hosts a nondegenerate minimal surface (of this simple form); but each of the duoprism kaleidoscopes gives at least one.<\/p>\n<p><strong>(2018)<\/strong> One could try minimal surfaces with the constraint of partitioning into equal volumes, if one understood how to specify such a constraint in non-Euclidean space.  Apparently it needs a metric tensor, whatever that is.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A few of the many triply periodic minimal surfaces can be generated from a quadrilateral slice through a tetrahedron of mirrors, as refined by Surface Evolver. I had the idea that the same concept, applied to one of the analogous &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=3114\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-3114","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3114","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3114"}],"version-history":[{"count":3,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3114\/revisions"}],"predecessor-version":[{"id":3889,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3114\/revisions\/3889"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}