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Could someone describe to me how to find the angle between two intersecting pentagonal faces on a great dodecahedron? Thanks

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Doesn't a great dodecahedron have triangular faces? A regular dodecahedron has pentagonal faces... –  mjqxxxx Dec 2 '11 at 4:01
    
There is an illustrative discussion of a comment similar to that of @mjqxxxx above in Proofs and refutations by Imre Lakatos on pp. 16--17 and pp. 30--33. –  Robert Haraway Dec 2 '11 at 6:13

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The answer is $$\arccos \frac{1}{\sqrt 5} \approx 63^\circ 26' 06'' \approx 1.107148718 \; \mbox{radians} $$ and thereby precisely supplementary to the dihedral angles of the ordinary dodecahedron.

The three books I have on this sort of thing are Platonic and Archimedean Solids by Daud Sutton, Shapes, Space, and Symmetry by Alan Holden, and Regular Polytopes by H. S. M. Coxeter. Sutton gives angles in degree-minute-second format, while Coxeter shows how to find them on pages 20-22.

http://en.wikipedia.org/wiki/Great_dodecahedron

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