{"id":606,"date":"2019-03-24T22:29:53","date_gmt":"2019-03-24T22:29:53","guid":{"rendered":"http:\/\/x-colony.com\/WorldPress\/?page_id=321"},"modified":"2019-04-16T19:46:15","modified_gmt":"2019-04-16T19:46:15","slug":"theorem-of-dihedral-angles","status":"publish","type":"page","link":"http:\/\/x-colony.com\/PoCo\/index.php\/activities\/theorems\/theorem-of-dihedral-angles\/","title":{"rendered":"Theorem of Dihedral Angles"},"content":{"rendered":"\n<p><strong>Theorem of Dihedral Angles<\/strong><br>The dihedral angle of a regular tetrahedron and the dihedral angle of a regular octahedron are supplementary.<\/p>\n\n\n\n<p><strong>Solution<br><\/strong>A constructive solution employs one (regular) octahedron and 4 <br>(regular) tetrahedra, all having the same side lengths.<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"357\" height=\"231\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-56-1.png\" alt=\"\" class=\"wp-image-362\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-56-1.png 357w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-56-1-300x194.png 300w\" sizes=\"(max-width: 357px) 85vw, 357px\" \/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n\n\n\n<p>Paste the tetrahedra onto the octahedron, such that each pair of tetrahedra shares no edge.<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"185\" height=\"188\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/03\/image-57.png\" alt=\"\" class=\"wp-image-363\"\/><figcaption>\n\t\t\t\t\t\t<\/figcaption><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Theorem of Dihedral AnglesThe dihedral angle of a regular tetrahedron and the dihedral angle of a regular octahedron are supplementary. SolutionA constructive solution employs one (regular) octahedron and 4 (regular) tetrahedra, all having the same side lengths. Paste the tetrahedra onto the octahedron, such that each pair of tetrahedra shares no edge.<\/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\/606"}],"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=606"}],"version-history":[{"count":2,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/606\/revisions"}],"predecessor-version":[{"id":857,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/606\/revisions\/857"}],"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=606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}