[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657904-105":59,"doc-detail-657904-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","whats-my-symmetry","What’s My Symmetry?","","Explains how to measure the number of symmetry directions for mirror-image versus radial symmetry, using the “fold” concept for symmetry axes or rotation steps. Applies the idea to a sixteen-sided round brilliant (SRB), clarifying why it is 8-fold mirror symmetry rather than 16-fold. Discusses how radial symmetry relates to rotation, the hierarchy between mirror and radial symmetries, and notes exceptions such as heart cuts. Connects symmetry classifications to practical consequences for gemstone index wheels and measuring feasible rotation steps.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/whats-my-symmetry/657904/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/whats-my-symmetry/657904.png","ImageObject",300,407,{"name":92,"@type":93},"Mimi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does “fold” mean for mirror-image symmetry and radial symmetry?","Question",{"text":112,"@type":113},"For mirror-image symmetry, “fold” measures the number of symmetry lines (axes). For radial symmetry, “fold” measures the number of steps needed for a full rotation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why is the standard round brilliant described as 8-fold mirror image symmetry instead of 16-fold?",{"text":117,"@type":113},"Each mirror placement corresponds to a line through a specific pair of opposite vertices, and there are only eight such vertex pairs. Mirrors across vertex 1–9 and 9–1 represent the same axis.",{"name":119,"@type":110,"acceptedAnswer":120},"How can the document explain radial symmetry using rotation by an eighth of a revolution?",{"text":121,"@type":113},"For the SRB, rotating the gem by 1/8 of a full turn produces an identical gem. The text also notes that mirror-image symmetry is assigned as the higher-order category in a hierarchy that places mirror-image above radial.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657904,1792993856,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":24},2336477974920,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","For both mirror-image and radial symmetry, there is a measure of how many directions of symmetry exist. This is where the 8-fold and 6-fold come in. The “fold” value measures the number of symmetry lines around the gem for mirror symmetry, or the number of steps to a full rotation for radial symmetry. For example, a sixteen-sided standard round brilliant design would look the same if you placed the mirror across any of the eight pairs of equally spaced opposite vertices. You can try it yourself with Figure 10- 16 on page 17. The SRB thus has “8-fold, mirror image symmetry.”  \nA couple of notes for the sharp-eyed reader. First, the SRB has 8-fold symmetry, not 16-fold symmetry. This is because each placement of the mirror corresponds to a line connecting a pair of vertices, and there are only eight such pairs. Effectively, placing the mirror between vertex 1 and vertex 9, say, is the same as placing the mirror between vertex 9 and vertex 1. It PZ HSZV LX\\P]HSLU[[V ÅPWWPUN [OL TPYYVY HYV\\UK 􀀘 􀀗􀂇􀀕  \nI know. You’re confused (heck – I’m confused) . Here’s another way to think about it. Imagine the mirror placed up-down, dividing the SRB design into left and right halves. Whether the shiny side of the mirror faces left (vertex 1 – vertex 9) or faces right (vertex 9 – vertex 1), the test answers the same question: does the left side look exactly like the right side ÅPWWLK V]LY& ;OPZ TLHZ\\YLment produces one symmetry axis, not two.  \nThe second note is more semantic than conceptual. The standard round brilliant actually has radial symmetry as well. Rotating the gem by an eighth of a revolution leaves you with an identical gem. Why is it assigned mirror-image symmetry? The unsatisfying answer is that it just is. At some level, you can consider the symmetries as a hierarchy, with mirror  \nimage above radial. A gemstone exhibiting both types  \nis labeled with the highest order of symmetry, in other words, mirror-image. Incidentally, not all gemstones with mirror-image symmetry have radial symmetry. The heart cut is a straightforward example.  \nPurists could argue that a heart, does, in fact, have one-fold radial symmetry. If you split a full rotation into N equal steps for N-fold radial symmetry, then one-fold corresponds to a complete rotation of 360°, bringing you back exactly to where you started. Of course, by [OPZ KLÄUP[PVU􀀓 L]LY` NLTZ[VUL 􀀏HUK PUKLLK L]LY` VIQLJ[ PU [OL \u003CUP]LYZL􀀐 OHZ VUL􀀔MVSK YHKPHS symmetry.  \nWhat’s My Symmetry?  \nHere’s a fun exercise. Reproduced below are the top views of several gem designs from Chapter 19. Try to !gure out each type of symmetry. You can !nd the answers in the cutting diagrams starting on page 334.  \nAll this talk of symmetry has some serious real-world consequences. The reason is that the symmetry of your gem design may be different from the symmetry of your index wheel.  \n-VY L_HTWSL􀀓 H NLTZ[VUL KLZPNU ^P[O Ä]L􀀔MVSK YHKPHS Z`TTL[Y` ^PSS OH]L MHJL[[PLYZ KPZ[YPI􀀔 uted every 72° around the gem, since 360 / 5 = 72. More than likely, your faceting machine has a 96-tooth index wheel, and thus you can measure angles in units of 360 / 96 = 3.75° . How do you make steps of 72° out of units of 3.75°? Do the math. You cannot. You would need 19.2 gear teeth on your machine to produce a rotation of 72° .  \nOops.","cbCais6DiFWQVtpp","https://ap.wps.com/l/cbCais6DiFWQVtpp","pdf",438247,"English","# What’s My Symmetry?\n## Measuring fold for mirror vs radial symmetry\n## Interpreting 8-fold symmetry in standard round brilliant\n## Radial symmetry, hierarchy, and exceptions\n## Real-world implications for index wheel angles","[{\"question\":\"What does “fold” mean for mirror-image symmetry and radial symmetry?\",\"answer\":\"For mirror-image symmetry, “fold” measures the number of symmetry lines (axes). For radial symmetry, “fold” measures the number of steps needed for a full rotation.\"},{\"question\":\"Why is the standard round brilliant described as 8-fold mirror image symmetry instead of 16-fold?\",\"answer\":\"Each mirror placement corresponds to a line through a specific pair of opposite vertices, and there are only eight such vertex pairs. Mirrors across vertex 1–9 and 9–1 represent the same axis.\"},{\"question\":\"How can the document explain radial symmetry using rotation by an eighth of a revolution?\",\"answer\":\"For the SRB, rotating the gem by 1/8 of a full turn produces an identical gem. The text also notes that mirror-image symmetry is assigned as the higher-order category in a hierarchy that places mirror-image above radial.\"}]","What’s My Symmetry? | PDF"]