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...cite arXiv|author=N Schmitt|title=Constant Mean Curvature ''n''-noids with Platonic Symmetries|eprint=math/0702469|year=2007}}</ref> ...n-de|accessdate=2012-10-05}}</ref> k-noids corresponding to the [[platonic solids]] and k-noids with handles.<ref>{{cite journal|author=Jorgen Berglund, Wayn ...

...cubes]]. Descartes introduced the study of figurate numbers based on the [[Platonic solid]]s and some [[Semiregular polyhedron|semiregular polyhedra]]; his wor ...

...pplicability) that Euler's formula itself holds true for the five Platonic solids.{{r|friedman}} ...wo-dimensional [[polygon]]s. In this part Descartes uses both the Platonic solids and some of the [[semiregular polyhedron|semiregular polyhedra]], but not t ...

...s">{{cite web |last1=Seaton |first1=K. A. |title=Platonicons: The Platonic Solids Start Rolling |url=http://archive.bridgesmathart.org/2020/bridges2020-371.h ...t each one of them circumscribes one of the five [[Platonic solid|Platonic solids]]. Unlike the other families, this family is not infinite. 14 Platonicons h ...

...cubes]]. Descartes introduced the study of figurate numbers based on the [[Platonic solid]]s and some [[Semiregular polyhedron|semiregular polyhedra]]; his wor ...

...]]. There are eighteen convex uniform prisms based on the [[Platonic solid|Platonic]] and [[Archimedean solid]]s ([[tetrahedral prism]], [[truncated tetrahedra ...

| footer = Historical [[crystal model]]s of slightly chamfered [[Platonic solid]]s == Chamfered Platonic solids == ...

...nvex]], non-[[stellation|stellated]]) [[regular icosahedron]]—one of the [[Platonic solid]]s—whose faces are 20 [[equilateral triangle]]s. ...ferred to simply as the ''regular icosahedron'', one of the five regular [[Platonic solid]]s, and is represented by its [[Schläfli symbol]] {3, 5}, containing ...

...ere can be considered to have an infinite number of sides. All six regular solids share many symmetries. ...

...tions. These groups have many uses, including producing the rotations of [[Platonic solid]]s and tessellating the plane. ...

The graphs of the [[Platonic solid]]s have been called ''Platonic graphs''. As well as having all the other properties of polyhedral graphs, ...

==== Solids ==== ...dron]] [[Cell (geometry)|cell]], the simplest [[uniform polyhedron]] and [[Platonic solid]], is made up of a total of '''14''' [[Simplex#Elements|elements]]: 4 ...

..., Dover edition, {{isbn|0-486-61480-8}}, 3.6 6.2 ''Stellating the Platonic solids'', pp.96-104 ...

...ce. The most prominent among these are the five [[Platonic solids|Platonic Solids]], and the 4-dimensional polytopes related to the [[120-cell]] and the [[60 ...

...h other]]) from the definition; uniform polyhedra include [[Platonic solid|Platonic]] and [[Archimedean solid]]s as well as [[Prism (geometry)|prism]]s and [[a The Johnson solids are named after American mathematician [[Norman Johnson (mathematician)|Nor ...

Many other [[convex polyhedron|convex polyhedra]], including all five [[Platonic solid]]s, have been shown to have the ''Rupert property'': a copy of the po ...pass through a hole {{nowrap|in <math>P</math>.{{r|AllFive}}}} All five [[Platonic solid]]s—the cube, regular [[tetrahedron]], regular [[octahedron]],{{r|scri ...

..., Dover edition, {{ISBN|0-486-61480-8}}, 3.6 6.2 ''Stellating the Platonic solids'', pp.96-104 ...

...the golden ratio as well. There he discovered two simple occurrences in [[platonic solid]]s and their circumscribed spheres. ...

== Full-sphere systems: Platonic solids == The regular [[Platonic solid]]s are the only full-sphere layouts for which closed-form solutions f ...

...=493–535 }}</ref> The most famous examples of the polar duality provide [[Platonic solid]]s: e.g., the [[cube]] is dual to [[octahedron]], the [[dodecahedron] ...