Disdyakis triacontahedron
Basic Geometry
The 3 edge lengths are:
- e1 : $ \frac{22 \sqrt{- \sqrt{5} + 5}}{5 \sqrt{- 31 \sqrt{5} + 85}} $ ≈ 1.847
- e2 : $ \frac{3 \sqrt{19 \sqrt{5} + 65}}{5 \sqrt{- 31 \sqrt{5} + 85}} $ ≈ 1.571
- e3 : $ 1 $ ≈ 1.000
The 3 angles are:
- α1 : $ \arccos{\left (\frac{5 \sqrt{- 31 \sqrt{5} + 85} \left(- \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + 1 + \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{44 \sqrt{- \sqrt{5} + 5}} \right )} $ ≈ 58.2379°
- α2 : $ \arccos{\left (\frac{25 \left(- 31 \sqrt{5} + 85\right) \left(-1 + \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{132 \sqrt{- \sqrt{5} + 5} \sqrt{19 \sqrt{5} + 65}} \right )} $ ≈ 32.7703°
- α3 : $ \arccos{\left (\frac{5 \sqrt{- 31 \sqrt{5} + 85} \left(- \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + 1 + \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{6 \sqrt{19 \sqrt{5} + 65}} \right )} $ ≈ 88.9918°
Further Properties
Dihedral angles:
- Minimal concave angle: 75.0000°
- Minimal convex angle: 75.0000°
Reversed edges: None
3D View
Show model in 3D viewer.
Similar Shapes
Model Files
Available gap values:- 0.2mm: disdyakis-triacontahedron-normal.stl
- 0.25mm: disdyakis-triacontahedron-normal.stl
- 0.4mm: disdyakis-triacontahedron-normal.stl
To download all files in one big package, see the download page.