{"id":609,"date":"2019-03-25T16:21:21","date_gmt":"2019-03-25T16:21:21","guid":{"rendered":"http:\/\/x-colony.com\/WorldPress\/?page_id=419"},"modified":"2019-04-16T19:43:15","modified_gmt":"2019-04-16T19:43:15","slug":"theorem-o-tessellation","status":"publish","type":"page","link":"http:\/\/x-colony.com\/PoCo\/index.php\/activities\/theorems\/theorem-o-tessellation\/","title":{"rendered":"Theorem O-Tessellation"},"content":{"rendered":"\n<p><strong>Theorem O-Tessellation<\/strong><\/p>\n\n\n\n<p>There exists a tessellation of the entire 3D space with truncated regular octahedra.<\/p>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>Construct 2 OTC modules: a red one and a blue one.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"292\" height=\"175\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-75.png\" alt=\"\" class=\"wp-image-421\"\/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n\n\n\n<p>Promote the blue module to the default <strong>Build <\/strong>module (double click on its name in the list) and generate the lattice shown below (using <strong>Nabla <\/strong>operations).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"520\" height=\"251\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-76-1.png\" alt=\"\" class=\"wp-image-424\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-76-1.png 520w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-76-1-300x145.png 300w\" sizes=\"(max-width: 520px) 85vw, 520px\" \/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n\n\n\n<p>Promote the red module to the default <strong>Build <\/strong>module and use it to generate the lattice shown (using <strong>Gamma <\/strong>operations).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"518\" height=\"281\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-77-1.png\" alt=\"\" class=\"wp-image-426\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-77-1.png 518w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-77-1-300x163.png 300w\" sizes=\"(max-width: 518px) 85vw, 518px\" \/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n\n\n\n<p>Rotate the ensemble to notice that the red modules are connected with <strong>Nabla <\/strong>operations.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"454\" height=\"282\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-78.png\" alt=\"\" class=\"wp-image-427\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-78.png 454w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-78-300x186.png 300w\" sizes=\"(max-width: 454px) 85vw, 454px\" \/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n\n\n\n<p> <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Theorem O-Tessellation There exists a tessellation of the entire 3D space with truncated regular octahedra. Solution Construct 2 OTC modules: a red one and a blue one. Promote the blue module to the default Build module (double click on its name in the list) and generate the lattice shown below (using Nabla operations). Promote the &hellip; <a href=\"http:\/\/x-colony.com\/PoCo\/index.php\/activities\/theorems\/theorem-o-tessellation\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Theorem O-Tessellation&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":80,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/609"}],"collection":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/comments?post=609"}],"version-history":[{"count":6,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/609\/revisions"}],"predecessor-version":[{"id":855,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/609\/revisions\/855"}],"up":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/80"}],"wp:attachment":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/media?parent=609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}