# Disdyakis dodecahedron

## Basic Geometry

The 3 edge lengths are:
• e1 : $\frac{\sqrt{2 \sqrt{2} + 20}}{\sqrt{- \sqrt{2} + 10}}$ ≈ 1.631
• e2 : $\frac{3 \sqrt{2 \sqrt{2} + 4}}{2 \sqrt{- \sqrt{2} + 10}}$ ≈ 1.338
• e3 : $1$ ≈ 1.000
The 3 angles are:
• α1 : $\arccos{\left (\frac{\sqrt{- \sqrt{2} + 10} \left(- \frac{9 \left(2 \sqrt{2} + 4\right)}{4 \left(- \sqrt{2} + 10\right)} + 1 + \frac{2 \sqrt{2} + 20}{- \sqrt{2} + 10}\right)}{2 \sqrt{2 \sqrt{2} + 20}} \right )}$ ≈ 55.0247°
• α2 : $\arccos{\left (\frac{\left(- \sqrt{2} + 10\right) \left(-1 + \frac{9 \left(2 \sqrt{2} + 4\right)}{4 \left(- \sqrt{2} + 10\right)} + \frac{2 \sqrt{2} + 20}{- \sqrt{2} + 10}\right)}{3 \sqrt{2 \sqrt{2} + 4} \sqrt{2 \sqrt{2} + 20}} \right )}$ ≈ 37.7733°
• α3 : $\arccos{\left (\frac{\sqrt{- \sqrt{2} + 10} \left(- \frac{2 \sqrt{2} + 20}{- \sqrt{2} + 10} + 1 + \frac{9 \left(2 \sqrt{2} + 4\right)}{4 \left(- \sqrt{2} + 10\right)}\right)}{3 \sqrt{2 \sqrt{2} + 4}} \right )}$ ≈ 87.2020°

## 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: