Great dodecicosacron

File:Great dodecicosacron.stl

3D model of a 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.

Proportions

Each face has two angles of $\arccos (\frac{3}{4}+\frac{1}{20}\sqrt{5})\approx 30.48032456536^{\circ }$ and two angles of $\arccos (-\frac{5}{12}+\frac{1}{4}\sqrt{5})\approx 81.816127508183^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos (\frac{5}{12}-\frac{1}{60}\sqrt{5})\approx 67.70354792646^{\circ }$. The dihedral angle equals $\arccos (\frac{-44+3\sqrt{5}}{61})\approx 127.68652342748^{\circ }$. The ratio between the lengths of the long edges and the short ones equals $\frac{1}{2}+\frac{1}{2}\sqrt{5}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

External links

• Uniform polyhedra and duals