{"id":43226,"date":"2025-04-27T11:55:07","date_gmt":"2025-04-27T11:55:07","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=43226"},"modified":"2025-04-27T11:55:07","modified_gmt":"2025-04-27T11:55:07","slug":"dihedral","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2025\/04\/27\/dihedral\/","title":{"rendered":"Dihedral"},"content":{"rendered":"<p><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-0.mp3\">Dihedral-0.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-0.mp4\">Dihedral-0.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-I.mp3\">Dihedral-I.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-I.mp4\">Dihedral-I.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-Reggae.mp3\">Dihedral-Reggae.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-Reggae.mp4\">Dihedral-Reggae.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-Unplugged-Underground-XVIII.mp3\">Dihedral-Unplugged-Underground-XVIII.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-Unplugged-Underground-XVIII.mp4\">Dihedral-Unplugged-Underground-XVIII.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XII\/Dihedral-intro.mp3\">Dihedral-intro.mp3<\/a><\/p>\n<p>[Intro]<br \/>\nDihedral triangular<br \/>\n(Can your mind&#8217;s eye see&#8230;)<br \/>\nIn 3D<br \/>\n[Bridge]<br \/>\n(da, dee, dee)<br \/>\nUp the bid<br \/>\n(Build a pyramid)<\/p>\n<p>[Verse 1]<br \/>\nWill your base<br \/>\nTake a side<br \/>\nThe human race<br \/>\nShall decide<\/p>\n<p>[Bridge]<br \/>\nDihedral triangular<br \/>\n(Can your mind&#8217;s eye see&#8230;)<br \/>\nIn 3D (da, dee, dee)<\/p>\n<p>[Chorus]<br \/>\nCastles of your dreams<br \/>\n(Make things what they seem)<br \/>\nTurning dreams to scenes<br \/>\n(Sower of seeds and seams)<\/p>\n<p>[Bridge]<br \/>\nBuild a pyramid<br \/>\n(We did!)<br \/>\n(Pyramid)<\/p>\n<p>[Verse 2]<br \/>\nAll sides hold us together<br \/>\nProud to report (group support)<br \/>\nHope resides in whether<br \/>\nWe resort (in our last hope)<\/p>\n<p>[Bridge]<br \/>\nDihedral triangular<br \/>\n(Can your mind&#8217;s eye see&#8230;)<br \/>\nIn 3D (dee, dee)<\/p>\n<p>[Chorus]<br \/>\nCastles of your dreams<br \/>\n(Make things what they seem)<br \/>\nTurning dreams to scenes<br \/>\n(Sower of seeds and seams)<\/p>\n<p>[Outro]<br \/>\nTurning dreams to scenes<br \/>\n(Turning dreams to scenes seen)<\/p>\n<p>A MATH AND SCIENCE NOTE<\/p>\n<h3 class=\"\" data-start=\"613\" data-end=\"663\"><strong data-start=\"621\" data-end=\"632\">Pyramid<\/strong> (like a square-based pyramid):<\/h3>\n<ul data-start=\"664\" data-end=\"1199\">\n<li class=\"\" data-start=\"664\" data-end=\"785\">\n<p class=\"\" data-start=\"666\" data-end=\"785\">Think of a <strong data-start=\"677\" data-end=\"689\">3D shape<\/strong> with a base (usually a square) and triangular sides that meet at a single top point (the apex).<\/p>\n<\/li>\n<li class=\"\" data-start=\"786\" data-end=\"846\">\n<p class=\"\" data-start=\"788\" data-end=\"846\">The faces (the sides) are usually <strong data-start=\"822\" data-end=\"845\">isosceles triangles<\/strong>.<\/p>\n<\/li>\n<li class=\"\" data-start=\"847\" data-end=\"1199\">\n<p class=\"\" data-start=\"849\" data-end=\"873\"><strong data-start=\"849\" data-end=\"872\">Angles in a pyramid<\/strong>:<\/p>\n<ul data-start=\"876\" data-end=\"1199\">\n<li class=\"\" data-start=\"876\" data-end=\"975\">\n<p class=\"\" data-start=\"878\" data-end=\"975\">The <strong data-start=\"882\" data-end=\"897\">base angles<\/strong> of the triangular sides are <strong data-start=\"926\" data-end=\"945\">typically equal<\/strong> (like an isosceles triangle).<\/p>\n<\/li>\n<li class=\"\" data-start=\"978\" data-end=\"1119\">\n<p class=\"\" data-start=\"980\" data-end=\"1119\">The <strong data-start=\"984\" data-end=\"1021\">angles between the base and sides<\/strong> (called <strong data-start=\"1030\" data-end=\"1049\">dihedral angles<\/strong>) are important in 3D \u2014 they control how steep or flat the pyramid is.<\/p>\n<\/li>\n<li class=\"\" data-start=\"1122\" data-end=\"1199\">\n<p class=\"\" data-start=\"1124\" data-end=\"1199\">The triangles themselves have angles depending on the slope of the pyramid.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1201\" data-end=\"1361\">So pyramids are <strong data-start=\"1217\" data-end=\"1251\">made up of isosceles triangles<\/strong>, and their structure involves a mix of <strong data-start=\"1291\" data-end=\"1307\">plane angles<\/strong> (in the triangles) and <strong data-start=\"1331\" data-end=\"1344\">3D angles<\/strong> (between faces).<\/p>\n<h3>From the album &#8220;<a href=\"\/songwriter\/tag\/angle\/\">Angle<\/a>&#8220;<\/h3>\n<h3>Also found on the album &#8220;<a href=\"\/songwriter\/tag\/reggae-spray\/\">Reggae Spray<\/a>&#8220;<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Dihedral-0.mp3 Dihedral-0.mp4 Dihedral-I.mp3 Dihedral-I.mp4 Dihedral-Reggae.mp3 Dihedral-Reggae.mp4 Dihedral-Unplugged-Underground-XVIII.mp3 Dihedral-Unplugged-Underground-XVIII.mp4 Dihedral-intro.mp3 [Intro] Dihedral triangular (Can your mind&#8217;s eye see&#8230;) In 3D [Bridge] (da, dee, dee) Up the bid (Build a pyramid) [Verse 1] Will your base Take a side The human race Shall decide [Bridge] Dihedral triangular (Can your mind&#8217;s eye see&#8230;) In 3D (da, dee, dee) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,9,14,17],"tags":[4120,4114],"class_list":["post-43226","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-daniel","category-lyrics","category-narley-marley-reggae","tag-angle","tag-reggae-spray"],"_links":{"self":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/43226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=43226"}],"version-history":[{"count":3,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/43226\/revisions"}],"predecessor-version":[{"id":43249,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/43226\/revisions\/43249"}],"wp:attachment":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=43226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=43226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=43226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}