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Great ditrigonal dodecacronic hexecontahedron

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Polyhedron with 60 faces
Great ditrigonal dodecacronic hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 44 (χ = −16)
Symmetry group Ih, , *532
Index references DU42
dual polyhedron Great ditrigonal dodecicosidodecahedron
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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