[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-74995-en":3,"doc-seo-74995-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},74995,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Pull-up Patterned Polyhedra for the Classroom","A classroom workshop introduces a simple, low-material method for making pull-up Platonic solids using only card nets and string. The approach addresses common difficulties students face when visualizing 3D shapes from 2D nets, reducing frustration and improving understanding through physical assembly and manipulation. Learners construct five patterned pull-up nets for tetrahedron, cube, octahedron, dodecahedron, and icosahedron, and explore extensions to other polyhedra and cross-curricular art-mathematics connections.","# Pull-up Patterned Polyhedra:\n\nPlatonic Solids forthe Classroom  \nE.B. Meenan* and B.G. ThomasSchool of Education* and School of DesignUniversity of LeedsLeeds, LS2 9JTe.b.meenan@leeds.ac.uk  \n## Abstract\n\nDrawing from many years of experience in the teaching of geometry, this workshop presents a simple method formaking pull-up Platonic solids in the classroom (requiring only card nets and string) . Workshop participants willhave the opportunity to make pull-up Platonic solids for themselves. Further possibilities for the creation of pull-upnets for other polyhedra will also be discussed.  \n## Introduction\n\nIt is a well-known problem that students find the visualization of three-dimensional shapes challenging,which leads to difficulties when teaching the names and characteristics of polyhedra. The traditionalmethod for creating shapes from two-dimensional nets, where students first try to visualize how the netfolds into the three-dimensional shape and then physically construct the polyhedron, can be problematic.Invariably pupils will devote much time and effort to the exercise but will often accidentally cut off thetabs and forget or misunderstand which edges must be glued together, resulting in anguish, frustration andan unsatisfactory outcome.  \nGeometry is an area of mathematics that appeals to many students, particularly visual thinkers. Thesestudents are often among those who either find math difficult or are disinterested in the subject. On theother hand, not all students who are good at traditional school mathematics are good at spatial work. Thisworkshop (see [1] for further ideas) has been designed to promote the teaching of two- and three -dimensional geometry in ways that are visually stimulating for students of a wide range of abilities,between the ages of 10 and 16. The intention of this workshop is to present methods that will help engagemore able students in an area of mathematics that they may find difficult and at the same time, encouragestudents who find traditional school mathematics difficult.  \nThe aim of the workshop is to ensure that participants become familiar with the methods for makingpull-up polyhedra and that this will act as a stimulus in their own teaching which, in turn, will allow themto introduce curriculum innovations which help to:  \n• increase students’motivation and enjoyment of mathematics  \n• explore the beauty of mathematics  \n• make cross-curricular connections between art and mathematics  \n• develop spatial awareness and visualization skills from two- to three-dimensions  \n• broaden students’creative outlook and develop practical skills  \nUnder a teacher’s supervision, students are fully capable of assembling the models. This visual studyand physical manipulation of the nets increases a pupils understanding of space through the physicalassembly and visualization required. The material presented within this workshop can be combined in theteaching of a larger cross-curricula project between art and mathematics departments, which couldinclude subjects such as symmetry, pattern, tessellations, paper-folding and a study of Islamic geometricpatterns. This workshop is currently delivered to schools alongside a current exhibition of tilings andpolyhedra presented at the University of Leeds [2] . Participants in the workshop will have the opportunityto construct each of the five pull-up nets for the Platonic solids and discuss their applicability within aclassroom setting.  \n## The Development of Patterned Pull-up Nets\n\nIn 1994, mathematics educator Bob Vertes introduced Meenan to the idea of pull-up polyhedron nets.These nets could be created using only card and string (not a tab or glue stick in sight) and easily foldedup into beautiful, three-dimensional shapes within the hand (see Figure 1) . It was a “mathemagical”experience that Meenan wanted to share with others. Vertes had provided nets for the tetrahedron, cubeand octahedron but Meenan was keen to develop the complete set for use as ","cbCaimaoA0TFb4Pt","https://ap.wps.com/l/cbCaimaoA0TFb4Pt","pdf",678297,2,1,"English","en",105,"# Abstract\n# Introduction\n# The Development of Patterned Pull-up Nets","[{\"question\":\"What materials are needed to make pull-up Platonic solids in the classroom workshop?\",\"answer\":\"Participants use card nets and string only. No tabs or glue stick are required for the pull-up net method described.\"},{\"question\":\"Why do students often struggle with teaching polyhedra using traditional 2D nets?\",\"answer\":\"Students face challenges visualizing how a net folds into a 3D solid, and they may cut off tabs or confuse which edges must be glued together, leading to frustration and unsatisfactory outcomes.\"},{\"question\":\"What does the workshop help participants achieve beyond assembling the models?\",\"answer\":\"It develops engagement and enjoyment of mathematics, encourages exploration of mathematical beauty, supports cross-curricular links between art and mathematics, and strengthens spatial awareness and visualization skills from 2D to 3D.\"}]",1784059108,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"pull-up-patterned-polyhedra-for-the-classroom","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,46,49],{"item":40,"name":41,"@type":42,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":20},"https://docshare.wps.com/document/","Document",{"item":47,"name":12,"@type":42,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/pull-up-patterned-polyhedra-for-the-classroom/74995/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-23","2026-07-14",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What materials are needed to make pull-up Platonic solids in the classroom workshop?","Question",{"text":74,"@type":75},"Participants use card nets and string only. No tabs or glue stick are required for the pull-up net method described.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Why do students often struggle with teaching polyhedra using traditional 2D nets?",{"text":79,"@type":75},"Students face challenges visualizing how a net folds into a 3D solid, and they may cut off tabs or confuse which edges must be glued together, leading to frustration and unsatisfactory outcomes.",{"name":81,"@type":72,"acceptedAnswer":82},"What does the workshop help participants achieve beyond assembling the models?",{"text":83,"@type":75},"It develops engagement and enjoyment of mathematics, encourages exploration of mathematical beauty, supports cross-curricular links between art and mathematics, and strengthens spatial awareness and visualization skills from 2D to 3D.","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,126,129,133],{"id":21,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":28,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":28,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]