Small hexagrammic hexecontahedron

Its faces are hexagonal stars with two short and four long edges. Denoting the golden ratio by $\backslash phi$ and putting $\backslash xi\; =\; \backslash frac\{1\}\{4\}+\backslash frac\{1\}\{4\}\backslash sqrt\{1+4\backslash phi\}\backslash approx\; 0.933\backslash ,380\backslash ,199\backslash ,59$, the stars have five equal angles of $\backslash arccos(\backslash xi)\backslash approx\; 21.031\backslash ,988\backslash ,967\backslash ,51^\{\backslash circ\}$ and one of $360^\{\backslash circ\}-\backslash arccos(\backslash phi^\{-2\}\backslash xi-\backslash phi^\{-1\})\backslash approx\; 254.840\backslash ,055\backslash ,162\backslash ,43^\{\backslash circ\}$. Each face has four long and two short edges. The ratio between the edge lengths is

:$1/2\; -1/2\backslash times\backslash sqrt\{(1-\backslash xi)/(\backslash phi^\{3\}-\backslash xi)\}\backslash approx\; 0.428\backslash ,986\backslash ,992\backslash ,12$.

The dihedral angle equals $\backslash arccos(\backslash xi/(1+\backslash xi))\backslash approx\; 61.133\backslash ,452\backslash ,273\backslash ,64^\{\backslash circ\}$. Part of each face is inside the solid, hence is not visible 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}}

• {{mathworld | urlname = SmallHexagrammicHexecontahedron| title =Small hexagrammic hexecontahedron}}

Category:Dual uniform polyhedra

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