Archimedean Solids

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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. The earliest surviving manuscript of this work dates from the tenth century and is identified as Codex Vaticanus Graecus 218. A photograph of a pair of pages from this manuscript can be downloaded from a Web site of the Library of Congress Vatican Exhibit (205 kilobytes, 1685 x 1249 pixels).

This manuscript gives the first known mention of the thirteen "Archimedean solids", which Pappus lists and attributes to Archimedes. The figures in the translation below and the modern names under them do not appear in Pappus's manuscript. These figures are from a World Wide Web site maintained by Tom Gettys . This site contains much interesting information about polyhedral solids and their geometrical and practical construction.

The translation begins . . .

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, the first contained by eight triangles and six squares,

Truncated Octahedron
the second by six squares and eight hexagons,
Truncated Cube
and the third by eight triangles and six octagons.

After these come two figures of twenty-six bases, the first contained by eight triangles and eighteen squares,
Truncated Cuboctahedron
the second by twelve squares, eight hexagons and six octagons.

After these come three figures of thirty-two bases, the first contained by twenty triangles and twelve pentagons,
Truncated Icosahedron
the second by twelve pentagons and twenty hexagons,

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

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. This book also contains the original Greek text.