{"id":923,"date":"2026-07-29T21:13:05","date_gmt":"2026-07-29T21:13:05","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/some-remarks-regarding-rhombic-polyhedra\/"},"modified":"2026-07-29T21:33:12","modified_gmt":"2026-07-29T21:33:12","slug":"some-remarks-regarding-rhombic-polyhedra","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/some-remarks-regarding-rhombic-polyhedra\/","title":{"rendered":"Some remarks regarding rhombic polyhedra"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>BRONIS\u0141AW PABICH<\/em><br><small>Wy\u017csza Szko\u0142a Nauk Pedgogicznych Warszawa, wieliczka<\/small><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Spatial geometry continues to conceal various secrets from its researchers. Sometimes, chance observations confirmed by the reading of metric quantities lead to discoveries in 3D geometry. Our students, unfamiliar with stereometry, can experience delightful moments of discovering facts that even their teachers are unaware of. Further discoveries stem from the search for analogies to already known knowledge.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here's an example that might confirm this thesis.<br>Let the students measure the angle \u03b1 at which we see the edge of a cube from its center, and then let's construct 12 congruent rhombuses whose acute angle has exactly this measure \u03b1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Then let the students assemble these 12 rhombuses into a convex polyhedron. Experts in 3D geometry know that this will produce the rhombic dodecahedron \u2013 one of the well-known rhombic hexahedrons.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"894\" height=\"406\" src=\"https:\/\/home.pf.jcu.cz\/~csgg2026\/wp-content\/uploads\/2026\/07\/Bronek_Fig-1.png\" alt=\"\" class=\"wp-image-935\" style=\"aspect-ratio:2.2020812353138637;width:610px;height:auto\" srcset=\"https:\/\/home.pf.jcu.cz\/~csgg2026\/wp-content\/uploads\/2026\/07\/Bronek_Fig-1.png 894w, https:\/\/home.pf.jcu.cz\/~csgg2026\/wp-content\/uploads\/2026\/07\/Bronek_Fig-1-300x136.png 300w, https:\/\/home.pf.jcu.cz\/~csgg2026\/wp-content\/uploads\/2026\/07\/Bronek_Fig-1-768x349.png 768w\" sizes=\"auto, (max-width: 894px) 100vw, 894px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Let's challenge students to continue their discoveries by asking, \"What should we do next?\"<br>Students might solve the same problem with other regular polyhedra and discover other rhombohedra.<br>\u2022 Which platonic polyhedra will they use for this purpose?<br>\u2022 What will they get from them?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The author of this talk will show the further history of this small 3D discovery. He will also show the corresponding 3D-printed models.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>BRONIS\u0141AW PABICHWy\u017csza Szko\u0142a Nauk Pedgogicznych Warszawa, wieliczka Spatial geometry continues to conceal various secrets from its researchers. Sometimes, chance observations confirmed by the reading of metric quantities lead to discoveries in 3D geometry. Our students, unfamiliar with stereometry, can experience delightful moments of discovering facts that even their teachers are unaware of. Further discoveries stem [&hellip;]<\/p>\n","protected":false},"author":43,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-923","post","type-post","status-publish","format-standard","hentry","category-presentations"],"_links":{"self":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/923","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/users\/43"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=923"}],"version-history":[{"count":5,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/923\/revisions"}],"predecessor-version":[{"id":936,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/923\/revisions\/936"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=923"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=923"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=923"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}