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Small dodecicosacron

From Wikipedia, the free encyclopedia
Small dodecicosacron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 32 (χ = −28)
Symmetry group Ih, [5,3], *532
Index references DU50
dual polyhedron Small dodecicosahedron
3D model of a small dodecicosacron

In geometry, the small dodecicosacron (or small dipteral trisicosahedron) is the dual of the small dodecicosahedron (U50). It is visually identical to the Small ditrigonal dodecacronic hexecontahedron. It has 60 intersecting bow-tie-shaped faces.

Proportions

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Each face has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals , which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

References

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  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
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Weisstein, Eric W. "Small dodecicosacron". MathWorld.