Great dodecicosacron

In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron (U₆₃). It has 60 intersecting bow-tie-shaped faces.

Great dodecicosacron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 32 (χ = −28)
Symmetry group	Ih, [5,3], *532
Index references	DU63
dual polyhedron	Great dodecicosahedron

3D model of a great dodecicosacron

Proportions

Each face has two angles of ${\displaystyle \arccos({\frac {3}{4}}+{\frac {1}{20}}{\sqrt {5}})\approx 30.480\,324\,565\,36^{\circ }}$ and two angles of ${\displaystyle \arccos(-{\frac {5}{12}}+{\frac {1}{4}}{\sqrt {5}})\approx 81.816\,127\,508\,183^{\circ }}$. The diagonals of each antiparallelogram intersect at an angle of ${\displaystyle \arccos({\frac {5}{12}}-{\frac {1}{60}}{\sqrt {5}})\approx 67.703\,547\,926\,46^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }}$. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {1}{2}}+{\frac {1}{2}}{\sqrt {5}}}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

References

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

External links

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

• Uniform polyhedra and duals