Archimedean Solids

Below is a translation from the fifth book of the "Collection" of the Greek mathematician Pappus of Alexandria, who lived in the beginning of the fourth century AD.

".... Although many solid figures having all kinds of surfaces can be conceived, those which appear to be regularly formed are most deserving of attention. Those include not only the five figures found in the godlike Plato, that is, the tetrahedron and the cube, the octahedron and the dodecahedron, and fifthly the icosahedron, but also the solids, thirteen in number, which were discovered by Archimedes and are contained by equilateral and equiangular, but not similar, polygons. ...."

Truncated Tetrahedron

 The first is a figure of eight bases, being contained by four triangles and four hexagons.
After this come three figures of fourteen bases,

Cuboctahedron

 the first contained by eight triangles and six squares,
Truncated Octahedron
the second by six squares and eight hexagons,sei quadrati e otto esagoni 		Truncated Cube
and the third by eight triangles and six octagons.
After these come two figures of twenty-six bases,

Rhombicuboctahedron
the first contained by eight triangles and eighteen squares,

Truncated Cuboctahedron
12 quadrati, otto esagoni e sei ottagoni.
After these come three figures of thirty-two bases
Icosidodecahedron


the first contained by twenty triangles and twelve pentagons,

Truncated Icosahedron
the second by twelve squares, eight hexagons and six octagons.
Truncated Dodecahedron
and the third by twenty triangles and twelve decagons. 		Snub Cube
After these comes one figure of thirty-eight bases, being contained by thirty-two triangles and six squares
Rhombicosidodecahedron
After this come two figures of sixty-two bases, the first contained by twenty triangles, thirty squares and twelve pentagons, 		Truncated Icosidodecahedron
the second by thirty squares, twenty hexagons and twelve decagons.
Snub Dodecahedron
After these there comes lastly a figure of ninety-two bases, which is contained by eighty triangles and twelve pentagons. 		   
Translation by Ivor Thomas in Greek Mathematical Works, Volume II (Aristarchus to Pappus of Alexandria), Loeb Classical Library, Harvard University Press, Cambridge, 1941, pages 195-197.

Images and text from the site: http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

Maggio 2022 - Contatti - Graziano Scotto di Clemente