Great rhombidodecacron

Each antiparallelogram has two angles of $\backslash arccos(\backslash frac\{1\}\{2\}+\backslash frac\{1\}\{5\}\backslash sqrt\{5\})\backslash approx\; 18.699\backslash ,407\backslash ,085\backslash ,15^\{\backslash circ\}$ and two angles of $\backslash arccos(-\backslash frac\{5\}\{8\}+\backslash frac\{1\}\{8\}\backslash sqrt\{5\})\backslash approx\; 110.211\backslash ,801\backslash ,805\backslash ,89^\{\backslash circ\}$. The diagonals of each antiparallelogram intersect at an angle of $\backslash arccos(\backslash frac\{1\}\{8\}+\backslash frac\{9\backslash sqrt\{5\}\}\{40\})\backslash approx\; 51.088\backslash ,791\backslash ,108\backslash ,96^\{\backslash circ\}$. The dihedral angle equals $\backslash arccos(\backslash frac\{-19+8\backslash sqrt\{5\}\}\{41\})\backslash approx\; 91.553\backslash ,403\backslash ,672\backslash ,16^\{\backslash circ\}$. The ratio between the lengths of the long edges and the short ones equals $\backslash frac\{1\}\{2\}+\backslash frac\{1\}\{2\}\backslash sqrt\{5\}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

• {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}} p. 88

• {{mathworld | urlname = GreatRhombidodecacron| title =Great pentagrammic hexecontahedron}}

Category:Dual uniform polyhedra

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