Polyhedron with 60 faces
3D model of a great ditrigonal dodecacronic hexecontahedron
In geometry , the great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron ) is a nonconvex isohedral polyhedron . It is the dual of the uniform great ditrigonal dodecicosidodecahedron . Its faces are kites . Part of each kite lies inside the solid, hence is invisible in solid models.
Proportions
Kite faces have two angles of
arccos
(
5
12
−
1
4
5
)
≈
98.183
872
491
81
∘
{\displaystyle \arccos({\frac {5}{12}}-{\frac {1}{4}}{\sqrt {5}})\approx 98.183\,872\,491\,81^{\circ }}
, one of
arccos
(
−
5
12
+
1
60
5
)
≈
112.296
452
073
54
∘
{\displaystyle \arccos(-{\frac {5}{12}}+{\frac {1}{60}}{\sqrt {5}})\approx 112.296\,452\,073\,54^{\circ }}
and one of
arccos
(
−
1
12
+
19
60
5
)
≈
51.335
802
942
83
∘
{\displaystyle \arccos(-{\frac {1}{12}}+{\frac {19}{60}}{\sqrt {5}})\approx 51.335\,802\,942\,83^{\circ }}
. Its dihedral angles equal
arccos
(
−
44
+
3
5
61
)
≈
127.686
523
427
48
∘
{\displaystyle \arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }}
. The ratio between the lengths of the long edges and the short ones equals
31
+
5
5
22
≈
1.917
288
176
70
{\displaystyle {\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70}
.
References
External links
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