Medial disdyakis triacontahedron

In geometry, the medial disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform truncated dodecadodecahedron. It has 120 triangular faces.

Medial disdyakis triacontahedron
Type	Star polyhedron
Face
Elements	F = 120, E = 180 V = 54 (χ = −6)
Symmetry group	Ih, [5,3], *532
Index references	DU59
dual polyhedron	Truncated dodecadodecahedron

3D model of a medial disdyakis triacontahedron

Proportions

The triangles have one angle of ${\displaystyle \arccos(-{\frac {1}{10}})\approx 95.739\,170\,477\,27^{\circ }}$, one of ${\displaystyle \arccos({\frac {3}{8}}+{\frac {11}{40}}{\sqrt {5}})\approx 8.142\,571\,179\,89^{\circ }}$ and one of ${\displaystyle \arccos(-{\frac {3}{8}}+{\frac {11}{40}}{\sqrt {5}})\approx 76.118\,258\,342\,85^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos(-{\frac {9}{11}})\approx 144.903\,198\,772\,42^{\circ }}$. Part of each triangle lies within 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. "Medial disdyakis triacontahedron". MathWorld.