# Angles for a great dodecahedron

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

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.