Rhombus 78

Fillygon rhombus-78 normal

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} + 7}}{\sqrt{\sqrt{5} + 5}} \right )} + \pi $ ≈ 101.8887°
  • α2 : $ 2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 7}}{\sqrt{\sqrt{5} + 5}} \right )} $ ≈ 78.1113°
  • α3 : $ - 2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 7}}{\sqrt{\sqrt{5} + 5}} \right )} + \pi $ ≈ 101.8887°
  • α4 : $ 2 \arctan{\left (\frac{\sqrt{- \sqrt{5} + 7}}{\sqrt{\sqrt{5} + 5}} \right )} $ ≈ 78.1113°

Further Properties

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

  • d1 : $ \frac{\sqrt{3} \sqrt{- \sqrt{5} + 7}}{3} $ ≈ 1.260
  • d2 : $ \frac{\sqrt{3} \sqrt{\sqrt{5} + 5}}{3} $ ≈ 1.553
and diagonal ratio:
  • d1 / d2 : $ \frac{\sqrt{- \sqrt{5} + 7}}{\sqrt{\sqrt{5} + 5}} $ ≈ 0.811

Dihedral angles:

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

Reversed edges: None

Similar Shapes

Model Files

Available gap values:

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