Rhombus 57

Fillygon rhombus-57 filled-corners

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°
Fillygon geometry of rhombus-57

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: 180.0000°
  • Minimal convex angle: 90.0000°

Reversed edges: None

3D View

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Similar Shapes

Model Files

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