{"id":5583,"date":"2025-10-12T22:56:25","date_gmt":"2025-10-12T22:56:25","guid":{"rendered":"https:\/\/www.novonon.com\/blog\/2025\/10\/12\/voderberg-tiling\/"},"modified":"2025-10-12T23:02:15","modified_gmt":"2025-10-12T23:02:15","slug":"voderberg-tiling","status":"publish","type":"post","link":"https:\/\/www.novonon.com\/blog\/2025\/10\/12\/voderberg-tiling\/","title":{"rendered":"Voderberg tiling"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"625\" height=\"554\" src=\"https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=625%2C554&#038;ssl=1\" alt=\"\" class=\"wp-image-5582\" srcset=\"https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=1024%2C907&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=300%2C266&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=150%2C133&amp;ssl=1 150w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=768%2C680&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?resize=624%2C553&amp;ssl=1 624w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?w=1354&amp;ssl=1 1354w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/voderberg-16716387315325360504.png?w=1250&amp;ssl=1 1250w\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>It is a monohedral tiling: it consists only of one shape that tessellates the plane with congruent copies of itself. In this case, the prototile is an elongated irregular nonagon, or nine-sided figure. The most interesting feature of this polygon is the fact that two copies of it can fully enclose a third one. E.g., the lowest purple nonagon is enclosed by two yellow ones, all three of identical shape.[4] Before Voderberg&#8217;s discovery, mathematicians had questioned whether this could be possible. <\/p>\n<\/blockquote>\n\n\n\n<p><\/p>\n\n\n\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Voderberg_tiling\">https:\/\/en.wikipedia.org\/wiki\/Voderberg_tiling<\/a><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Bonus tiling: <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"343\" src=\"https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/tilings_and_patterns_cover2501159254716276741.jpg?resize=290%2C343&#038;ssl=1\" alt=\"\" class=\"wp-image-5584\" srcset=\"https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/tilings_and_patterns_cover2501159254716276741.jpg?w=290&amp;ssl=1 290w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/tilings_and_patterns_cover2501159254716276741.jpg?resize=254%2C300&amp;ssl=1 254w, https:\/\/i0.wp.com\/www.novonon.com\/blog\/wp-content\/uploads\/2025\/10\/tilings_and_patterns_cover2501159254716276741.jpg?resize=127%2C150&amp;ssl=1 127w\" sizes=\"auto, (max-width: 290px) 100vw, 290px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>It is a monohedral tiling: it consists only of one shape that tessellates the plane with congruent copies of itself. In this case, the prototile is an elongated irregular nonagon, or nine-sided figure. The most interesting feature of this polygon is the fact that two copies of it can fully enclose a third one. E.g., [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-5583","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3pfIY-1s3","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts\/5583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/comments?post=5583"}],"version-history":[{"count":1,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts\/5583\/revisions"}],"predecessor-version":[{"id":5585,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts\/5583\/revisions\/5585"}],"wp:attachment":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/media?parent=5583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/categories?post=5583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/tags?post=5583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}