Great hexagonal hexecontahedron

{{Uniform polyhedra db|Uniform dual polyhedron stat table|Gisdid}}

File:Great hexagonal hexecontahedron.stl

In geometry, the great hexagonal hexecontahedron (or great astroid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great snub dodecicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar pentagrammic faces.

Proportions

The faces are nonconvex hexagons. Denoting the golden ratio by $\phi$ , the hexagons have one angle of $\arccos(-\phi^{-1})\approx 128.172\,707\,627\,01^{\circ}$ , one of $360^{\circ}-\arccos(-\phi^{-1})\approx 231.827\,292\,372\,99^{\circ}$ , and four angles of $90^{\circ}$ . They have two long edges, two of medium length and two short ones. If the long edges have length $2$ , the medium ones have length $1+\phi^{-3/2}\approx 1.485\,868\,271\,76$ and the short ones $1-\phi^{-3/2}\approx 0.514\,131\,728\,24$ . The dihedral angle equals $90^{\circ}$ .

References

{{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}}

External links

{{mathworld | urlname = GreatHexagonalHexecontahedron| title =Great hexagonal hexecontahedron}}

Category:Dual uniform polyhedra