# 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.

## Model Files

Available gap values: