Medial deltoidal hexecontahedron
Polyhedron with 60 faces
3D model of a medial deltoidal hexecontahedron
In geometry , the medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron . It is the dual of the rhombidodecadodecahedron . Its 60 intersecting quadrilateral faces are kites .
Proportions
The kites have two angles of
arccos
(
1
6
)
≈
80.405
931
773
14
∘
{\displaystyle \arccos({\frac {1}{6})\approx 80.405\,931\,773\,14^{\circ }
, one of
arccos
(
−
1
8
+
7
24
5
)
≈
58.184
446
117
59
∘
{\displaystyle \arccos(-{\frac {1}{8}+{\frac {7}{24}{\sqrt {5})\approx 58.184\,446\,117\,59^{\circ }
and one of
arccos
(
−
1
8
−
7
24
5
)
≈
141.003
690
336
13
∘
{\displaystyle \arccos(-{\frac {1}{8}-{\frac {7}{24}{\sqrt {5})\approx 141.003\,690\,336\,13^{\circ }
. The dihedral angle equals
arccos
(
−
5
7
)
≈
135.584
691
402
81
∘
{\displaystyle \arccos(-{\frac {5}{7})\approx 135.584\,691\,402\,81^{\circ }
. The ratio between the lengths of the long and short edges is
27
+
7
5
22
≈
1.938
748
901
931
75
{\displaystyle {\frac {27+7{\sqrt {5}{22}\approx 1.938\,748\,901\,931\,75}
. Part of each kite lies inside the solid, hence is invisible in solid models.
References
External links
Kepler-Poinsot polyhedra (nonconvex regular polyhedra)Uniform truncations of Kepler-Poinsot polyhedra Nonconvex uniform hemipolyhedra Duals of nonconvex uniform polyhedra Duals of nonconvex uniform polyhedra with infinite stellations
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