{"id":208,"date":"2012-07-18T06:23:21","date_gmt":"2012-07-18T11:23:21","guid":{"rendered":"http:\/\/daylateanddollarshort.com\/bloog\/?p=208"},"modified":"2012-07-18T06:23:21","modified_gmt":"2012-07-18T11:23:21","slug":"tetrahedra-sharing-volume-faces-areas-and-circumradius","status":"publish","type":"post","link":"http:\/\/daylateanddollarshort.com\/bloog\/tetrahedra-sharing-volume-faces-areas-and-circumradius\/","title":{"rendered":"Tetrahedra Sharing Volume, Faces Areas, and Circumradius"},"content":{"rendered":"<p>From the abstract of my note <a title=\"&quot;Tetrahedra Sharing Volume, Face Areas, and Circumradius: a Hedronometric Approach&quot; at the Bloog!\" href=\"http:\/\/daylateanddollarshort.com\/mathdocs\/Tetrahedra-Sharing-Volume-Face-Areas-and-Circumradius.pdf\">&#8220;Tetrahedra Sharing Volume, Face Areas, and Circumradius: A Hedronometric Approach&#8221;<\/a>:<\/p>\n<blockquote><p>Volume, face areas, and circumradius sometimes determine multiple &#8212;even infinitely-many&#8212; non-isomorphic tetrahedra. Hedronometry provides a context for unifying and streamlining previous discussions of this fact.<\/p><\/blockquote>\n<p>This was my first attempt to solve someone else&#8217;s problem with hedronometry. I&#8217;m rather pleased at how well hedronometry fit the circumstances, although I believe some of the subsequent polynomial analysis could use some finessing.<\/p>\n<p>The <strong>Open Question<\/strong>:<\/p>\n<blockquote><p>In the case of &#8220;doubly-bisohedral&#8221; tetrahedra (Section 2.3), is it ever possible to determine four or more non-isomorphic figures? (The best I can do is three.)<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>From the abstract of my note &#8220;Tetrahedra Sharing Volume, Face Areas, and Circumradius: A Hedronometric Approach&#8221;: Volume, face areas, and circumradius sometimes determine multiple &#8212;even infinitely-many&#8212; non-isomorphic tetrahedra. Hedronometry provides a context for unifying and streamlining previous discussions of this fact. This was my first attempt to solve someone else&#8217;s problem with hedronometry. I&#8217;m rather [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,11],"tags":[],"class_list":["post-208","post","type-post","status-publish","format-standard","hentry","category-hedronometry","category-open-question"],"_links":{"self":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/comments?post=208"}],"version-history":[{"count":1,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/208\/revisions"}],"predecessor-version":[{"id":209,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/208\/revisions\/209"}],"wp:attachment":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/media?parent=208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/categories?post=208"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/tags?post=208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}