Proof
The dodecahedron has twelve regular pentagonal faces; the side is
the apotome formed when the cube-edge is cut in extreme and mean
ratio (XIII.6). Inscribe by placing pentagonal faces on the six
square faces of the inscribed cube (XIII.15).
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Depends on (4)
- IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
- XIII.6Proposition XIII.6If a rational straight line be cut in extreme and mean ratio, each of the segments is the irrational straight line…
- XIII.15Proposition XIII.15To construct a cube and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
- XIII.16Proposition XIII.16To construct an icosahedron and comprehend it in a sphere, as in the case of the aforesaid figures; and to prove that…
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