{"id":2053,"date":"2008-03-11T22:45:15","date_gmt":"2008-03-12T06:45:15","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=2053"},"modified":"2021-10-08T11:11:52","modified_gmt":"2021-10-08T19:11:52","slug":"symmetries-made-simple","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=2053","title":{"rendered":"symmetries made simple"},"content":{"rendered":"<p>This may be of interest to only a few: <a href=\"http:\/\/dmccooey.com\/polyhedra\/Simplest.html\">Simplest Canonical Polyhedra of Each Symmetry Type<\/a> (rotable in Java); in other words, canonical forms of the simplest topologies that allow the specified symmetries and none higher.  Any convex polyhedron can be deformed into a &#8220;canonical&#8221; form whose edges are all tangent to a sphere; if a polyhedron is self-dual, it is canonical.<\/p>\n<p>This collection could be considered a generalization of the <a href=\"http:\/\/www.mathpuzzle.com\/Fairdice.htm\">set of all fair dice<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This may be of interest to only a few: Simplest Canonical Polyhedra of Each Symmetry Type (rotable in Java); in other words, canonical forms of the simplest topologies that allow the specified symmetries and none higher. Any convex polyhedron can &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=2053\">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-2053","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2053","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=2053"}],"version-history":[{"count":1,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2053\/revisions"}],"predecessor-version":[{"id":4238,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2053\/revisions\/4238"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}