{"id":2847,"date":"2018-07-08T16:50:54","date_gmt":"2018-07-08T15:50:54","guid":{"rendered":"http:\/\/www2.ual.es\/neotrie\/?p=2847"},"modified":"2026-05-27T11:45:23","modified_gmt":"2026-05-27T10:45:23","slug":"honeycombs","status":"publish","type":"post","link":"https:\/\/www2.ual.es\/neotrie\/honeycombs\/","title":{"rendered":"Honeycombs"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-1024x576.png\" alt=\"\" class=\"wp-image-2849\" srcset=\"https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-1024x576.png 1024w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-300x169.png 300w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-768x432.png 768w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-1536x864.png 1536w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2-1080x608.png 1080w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-55-09-2.png 1920w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">It is known that the bottom of honeycombs are rhombic dodecahedra (part of).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"576\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/799px-bienenwabe_mit_eiern_und_brut_5.jpg\" alt=\"\" class=\"wp-image-2854\" srcset=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/799px-bienenwabe_mit_eiern_und_brut_5.jpg 768w, http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/799px-bienenwabe_mit_eiern_und_brut_5-480x360.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 768px, 100vw\" \/><figcaption>Source:\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/File:Bienenwabe_mit_Eiern_und_Brut_5.jpg\">http:\/\/en.wikipedia.org\/wiki\/File:Bienenwabe_mit_Eiern_und_Brut_5.jpg<\/a><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The rhombic dodecahedron is one of the convex polyhedra that tessellates the space; see [Weisstein].<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"432\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-05-28_12-55-03.png\" alt=\"\" class=\"wp-image-2848\" srcset=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-05-28_12-55-03.png 768w, http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-05-28_12-55-03-480x270.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 768px, 100vw\" \/><figcaption>Tessellation of rhombic dodecahedra made by Antonio Zarauz (May 2018, NeoTrie VR).<br><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the video below we construct this cell of the honeycomb (which is flat on the top part) from a rhombic dodecahedron, using the tools of \u201cmiddle point\u201d, \u201cintersection\u201d, and \u201ccopy seal\u201d in NeoTrie VR.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"432\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-19.png\" alt=\"\" class=\"wp-image-2850\" srcset=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-19.png 768w, http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-19-480x270.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 768px, 100vw\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"432\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-46.png\" alt=\"\" class=\"wp-image-2851\" srcset=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-46.png 768w, http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-51-46-480x270.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 768px, 100vw\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"432\" src=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-54-29.png\" alt=\"\" class=\"wp-image-2853\" srcset=\"http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-54-29.png 768w, http:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2020\/05\/screen_1920x1080_2018-07-07_14-54-29-480x270.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 768px, 100vw\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"How to make a honeycomb - NeoTrie VR\" width=\"1080\" height=\"608\" src=\"https:\/\/www.youtube.com\/embed\/axxZysjjo-8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This video was made in the congress #17CEAMTHALES (<a href=\"http:\/\/thales.cica.es\/xviiceam\/\">http:\/\/thales.cica.es\/xviiceam\/)<\/a>, with Ana Garc\u00eda L\u00f3pez and Manuel Mart\u00ednez D\u00edaz, after a communication about their project \u201cALLAN POE O EL SECRETO DE LAS ABEJAS\u201d.<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Edgard Alan Poe o el secreto de las abejas\" width=\"1080\" height=\"608\" src=\"https:\/\/www.youtube.com\/embed\/0FfQiMD3xNA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">References:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ib\u00e1\u00f1ez R., El rombododecaedro estrellado: arte, abejas y puzzles, Cuaderno de Cultura Cient\u00edfica, 2014. Universidad del Pa\u00eds Vasco.&nbsp;<a href=\"https:\/\/culturacientifica.com\/2014\/02\/26\/el-rombododecaedro-estrellado-arte-abejas-y-puzzles-primera-parte\/\">https:\/\/culturacientifica.com\/2014\/02\/26\/el-rombododecaedro-estrellado-arte-abejas-y-puzzles-primera-parte\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cangas D., Crespo D., Grazyna M., Rodr\u00edguez J. L., Zarauz A., CONSTRUYENDO Y APRENDIENDO GEOMETR\u00cdA 3D EN REALIDAD VIRTUAL, Actas de XVII Congreso de Ense\u00f1anza y Aprendizaje de las Matem\u00e1ticas. Almer\u00eda 2018 (en prensa).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Weisstein, Eric W. \u201cSpace-Filling Polyhedron.\u201d From MathWorld\u2013A Wolfram Web Resource.&nbsp;<a href=\"http:\/\/mathworld.wolfram.com\/Space-FillingPolyhedron.html\">http:\/\/mathworld.wolfram.com\/Space-FillingPolyhedron.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[43],"tags":[69],"class_list":["post-2847","post","type-post","status-publish","format-standard","hentry","category-universidad","tag-teselaciones-3d"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"It is known that the bottom of honeycombs are rhombic dodecahedra (part of). 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