Great truncated icosidodecahedron

Great disdyakis triacontahedron
Type	Star polyhedron
Face
Elements	F = 120, E = 180 V = 62 (χ = 2)
Symmetry group	Ih, [5,3], *532
Index references	DU68
dual polyhedron	Great truncated icosidodecahedron

3D model of a great disdyakis triacontahedron

The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.

The triangles have one angle of ${\displaystyle \arccos({\frac {1}{6}}+{\frac {1}{15}}{\sqrt {5}})\approx 71.594\,636\,220\,88^{\circ }}$, one of ${\displaystyle \arccos({\frac {3}{4}}+{\frac {1}{10}}{\sqrt {5}})\approx 13.192\,999\,040\,74^{\circ }}$ and one of ${\displaystyle \arccos({\frac {3}{8}}-{\frac {5}{24}}{\sqrt {5}})\approx 95.212\,364\,738\,38^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-179+24{\sqrt {5}}}{241}})\approx 121.336\,250\,807\,39^{\circ }}$. Part of each triangle lies within the solid, hence is invisible in solid models.