In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter are themselves examples of Dupin cyclides. They were discovered c. 1802 by Charles Dupin, while he was still a student at the École polytechnique following Gaspard Monge's lectures. The key property of a Dupin cyclide is that it is a channel surface in two different ways. This property means that Dupin cyclides are natural objects in Lie sphere geometry.
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{"slip": { "id": 120, "advice": "A nod is as good as a wink to a blind horse."}}
{"fact":"Edward Lear, author of \\The Owl and the Pussycat\\\"\", is said to have had his new house in San Remo built to exactly the same specification as his previous residence, so that his much-loved tabby, Foss, would immediately feel at home.\"\"\"","length":236}
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{"type":"standard","title":"Roland Sapsford","displaytitle":"Roland Sapsford","namespace":{"id":0,"text":""},"wikibase_item":"Q7360430","titles":{"canonical":"Roland_Sapsford","normalized":"Roland Sapsford","display":"Roland Sapsford"},"pageid":21685700,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Roland_Sapsford.jpg/330px-Roland_Sapsford.jpg","width":320,"height":309},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/c/cb/Roland_Sapsford.jpg","width":584,"height":564},"lang":"en","dir":"ltr","revision":"1287429205","tid":"68dcf6dd-2260-11f0-ab95-ca99165620cb","timestamp":"2025-04-26T05:36:32Z","description":"New Zealand politician","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Roland_Sapsford","revisions":"https://en.wikipedia.org/wiki/Roland_Sapsford?action=history","edit":"https://en.wikipedia.org/wiki/Roland_Sapsford?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Roland_Sapsford"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Roland_Sapsford","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Roland_Sapsford","edit":"https://en.m.wikipedia.org/wiki/Roland_Sapsford?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Roland_Sapsford"}},"extract":"Roland Sapsford is a former male co-convenor of the Green Party of Aotearoa New Zealand. The female co-convenor in the latter