The thirteen archimedean solids are the polyhedra (other than the five regular solids) all the faces of which are regular polygons and where for each pair of vertices some symmetry transformation carries one vertex to the other (see 1st attached image).

According to Pappus (fl. c.300–c.350 CE), who wrote a half-millennium later, Archimedes discovered them. The context of Pappus' report suggests that Archimedes was seeking polyhedra inscribable in spheres.

Archimedes excluded the infinite classes of prisms and anti-prisms, in which two n-gons are joined by squares or equilateral triangles (2nd attached image). Although they satisfy the definition, and are technically inscribable in spheres, they are somehow not ‘sphere-like’.

This suggests that Archimedes may have been influenced by the aesthetic preference for circles and spheres that descended from Pythagoras.

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#ArchimedeanSolids #RegularSolids #polyhedra #Archimedes #Pappus #HistMath

Pure #CSS #3D chamfering sequence on @codepen cube → chamfered cube → rhombic dodecahedron and back

https://codepen.io/thebabydino/pen/rNdjLdq

Chamfer? WTF is that?

Well, check out the Pen description https://codepen.io/thebabydino/details/rNdjLdq and this page https://en.wikipedia.org/wiki/Chamfer_(geometry)

#Maths #geometry #css3D #transform #chamfer #polyhedron #polyhedra #cube #rhombicDodecahedron #code #coding #web #dev #webDev #webDevelopment

Pure #CSS #3D demo on @codepen: polyhedra morphing sequence https://codepen.io/thebabydino/pen/abmNveW

Absolutely no magic numbers, everything computed.

See Pen description for the how behind 😼

#transform #cssTransform #polyhedron #cssTransforms #polyhedra #octahedron #tetrahedron #cube #Maths #geometry #cssVariables #code #coding #frontend #web #dev #webDev #webDevelopment

Exploding triakis octahedron (short pyramids added on top of the faces) turning into an excavated octahedron (short pyramids dug into the faces) with pure #CSS #3D - live on @codepen: https://codepen.io/thebabydino/pen/DyrNrL

#Maths #geometry #polyhedra #css3D #cssTransform #cssTransforms #coding #code #transform #frontend #cssMaths #Sass #web #dev #webDevelopment #webDev #trigonometry #polyhedron #octahedron

One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe

A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.

#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS

Illustration by Max Brückner, from Vielecke und Vielflache: Theorie und Geschichte (1900).

Source: University of Toronto Libraries / Internet Archive

https://pdimagearchive.org/images/b507c4c1-b707-4bfb-8686-233de0340dfa

#mathematics #models #polyhedra #geometry #sculpture #art #publicdomain

Given that I am still re-reading the first page of this book for like the tenth time, I have doubts about “we can simply say”

#math #polyhedra #tron

Noperty:
#polyhedra #platonicsolids #shapes #geometry #mathematics
🤓

https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/

Illustration by Max Brückner, from Vielecke und Vielflache: Theorie und Geschichte (1900).

Source: University of Toronto Libraries / Internet Archive

https://pdimagearchive.org/images/7bd22905-64be-450b-89e4-92f723150de4

#mathematics #models #polyhedra #geometry #sculpture #art #publicdomain

I made another #papercraft Stewart toroid!

The convex hull (formed by all vertices touching blue faces) is a truncated cuboctahedron. Each octagonal face has a square cupola excavation (in red), and the core is an elongated square gyrobicupola (in purple).

The "gyro" in "gyrobicupola" refers to the fact that one face is at a 45 degree angle compared to the one antipodal, and this is reflected in the fact that one of the cupolae is rotated by the same amount.

#polyhedra #papercraft #math