{"id":917,"date":"2014-09-01T01:00:41","date_gmt":"2014-09-01T01:00:41","guid":{"rendered":"http:\/\/blogs.ams.org\/visualinsight\/?p=917"},"modified":"2015-07-29T00:50:19","modified_gmt":"2015-07-29T00:50:19","slug":"intersection-of-337-honeycomb-and-the-plane-at-infinity","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/visualinsight\/2014\/09\/01\/intersection-of-337-honeycomb-and-the-plane-at-infinity\/","title":{"rendered":"{3,3,7} Honeycomb Meets Plane at Infinity"},"content":{"rendered":"
\n
\"Intersection<\/a>

Intersection of {3,3,7} and the Plane at Infinity – Roice Nelson<\/p><\/div>\n<\/div>\n

 <\/p>\n

The {3,3,7} honeycomb<\/b> is a honeycomb in 3d hyperbolic space. It is the dual of the {7,3,3} honeycomb shown last time:<\/p>\n

• {7,3,3} honeycomb<\/a>.<\/p>\n

The image above, drawn by Roice Nelson, shows the ‘boundary’ of the {3,3,7} honeycomb: that is, the set of points on the ‘plane at infinity’ of hyperbolic space that are limits of points in the {3,3,7} honeycomb.<\/p>\n

Roice Nelson, the creator of this image, has a blog with lots of articles about geometry, and he makes plastic models of interesting geometrical objects using a 3d printer:<\/p>\n

\u2022 Roice<\/a>.<\/p>\n

\n

Visual Insight<\/i> is a place to share striking images that help explain advanced topics in mathematics. I\u2019m always looking for truly beautiful images, so if you know about one, please drop a comment here<\/a> and let me know!<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

The {3,3,7} honeycomb<\/b> is a honeycomb in 3d hyperbolic space. It is the dual of the {7,3,3} honeycomb shown last time<\/a>. This image, drawn by Roice Nelson, shows the ‘boundary’ of the {3,3,7} honeycomb: that is, the set of points on the ‘plane at infinity’ that are limits of points in the {3,3,7} honeycomb.<\/p>\n

<\/div>\n","protected":false},"author":66,"featured_media":969,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9,2],"tags":[],"class_list":["post-917","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-honeycombs","category-images-library"],"jetpack_featured_media_url":"https:\/\/blogs.ams.org\/visualinsight\/files\/2014\/06\/337_plane_at_infinity.png","jetpack_shortlink":"https:\/\/wp.me\/p42Vmc-eN","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/posts\/917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/comments?post=917"}],"version-history":[{"count":16,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/posts\/917\/revisions"}],"predecessor-version":[{"id":1045,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/posts\/917\/revisions\/1045"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/media\/969"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/media?parent=917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/categories?post=917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/visualinsight\/wp-json\/wp\/v2\/tags?post=917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}