Small rhombidodecacron
60-sided polyhedron
3D model of a small rhombidodecacron
In geometry , the small rhombidodecacron is a nonconvex isohedral polyhedron . It is the dual of the small rhombidodecahedron . It is visually identical to the Small dodecacronic hexecontahedron . It has 60 intersecting antiparallelogram faces.
Proportions
Each face has two angles of
arccos
(
5
8
+
1
8
5
)
≈
25.242
832
961
52
∘
{\displaystyle \arccos({\frac {5}{8}+{\frac {1}{8}{\sqrt {5})\approx 25.242\,832\,961\,52^{\circ }
and two angles of
arccos
(
−
1
2
+
1
5
5
)
≈
93.025
844
508
96
∘
{\displaystyle \arccos(-{\frac {1}{2}+{\frac {1}{5}{\sqrt {5})\approx 93.025\,844\,508\,96^{\circ }
. The diagonals of each antiparallelogram intersect at an angle of
arccos
(
1
4
+
1
10
5
)
≈
61.731
322
529
52
∘
{\displaystyle \arccos({\frac {1}{4}+{\frac {1}{10}{\sqrt {5})\approx 61.731\,322\,529\,52^{\circ }
. The ratio between the lengths of the long edges and the short ones equals
1
2
+
1
2
5
{\displaystyle {\frac {1}{2}+{\frac {1}{2}{\sqrt {5}
, which is the golden ratio . The dihedral angle equals
arccos
(
−
19
−
8
5
41
)
≈
154.121
363
125
78
∘
{\displaystyle \arccos({\frac {-19-8{\sqrt {5}{41})\approx 154.121\,363\,125\,78^{\circ }
.
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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