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Small dodecicosacron

Polyhedron with 60 faces From Wikipedia, the free encyclopedia

Small dodecicosacron
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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.

Small dodecicosacron
Thumb
TypeStar polyhedron
FaceThumb
ElementsF = 60, E = 120
V = 32 (χ = 28)
Symmetry groupIh, [5,3], *532
Index referencesDU50
dual polyhedronSmall dodecicosahedron
Thumb
3D model of a small dodecicosacron
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Proportions

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.

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References

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

Weisstein, Eric W. "Small dodecicosacron". MathWorld.

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