medial disdyakis triacontahedron

{{Short description|Polyhedron with 120 faces}}

{{Uniform polyhedra db|Uniform dual polyhedron stat table|tDD}}

File:Medial disdyakis triacontahedron.stl

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.

Proportions

The triangles have one angle of \arccos(-\frac{1}{10})\approx 95.739\,170\,477\,27^{\circ}, one of \arccos(\frac{3}{8}+\frac{11}{40}\sqrt{5})\approx 8.142\,571\,179\,89^{\circ} and one of \arccos(-\frac{3}{8}+\frac{11}{40}\sqrt{5})\approx 76.118\,258\,342\,85^{\circ}. The dihedral angle equals \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

  • {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 | mr= 730208| year=1983}}