# Rhombus 57

## Basic Geometry

The 4 edge lengths are:
• e1 : $1$ ≈ 1.000
• e2 : $1$ ≈ 1.000
• e3 : $1$ ≈ 1.000
• e4 : $1$ ≈ 1.000
The 4 angles are:
• α1 : $- 2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 5}}{\sqrt{\sqrt{5} + 7}} \right )} + \pi$ ≈ 122.6390°
• α2 : $2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 5}}{\sqrt{\sqrt{5} + 7}} \right )}$ ≈ 57.3610°
• α3 : $- 2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 5}}{\sqrt{\sqrt{5} + 7}} \right )} + \pi$ ≈ 122.6390°
• α4 : $2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 5}}{\sqrt{\sqrt{5} + 7}} \right )}$ ≈ 57.3610°

## Further Properties

This fillygon is a rhombus with short (d1) and long (d2) diagonals:

• d1 : $\frac{\sqrt{3} \sqrt{- \sqrt{5} + 5}}{3}$ ≈ 0.960
• d2 : $\frac{\sqrt{3} \sqrt{\sqrt{5} + 7}}{3}$ ≈ 1.755
and diagonal ratio:
• d1 / d2 : $\frac{\sqrt{- \sqrt{5} + 5}}{\sqrt{\sqrt{5} + 7}}$ ≈ 0.547

Dihedral angles:

• Minimal concave angle: 38.0000°
• Minimal convex angle: 38.0000°

Reversed edges: None

## 3D View

Show model in 3D viewer.

## Model Files

Available gap values: