Rhombus 42

Fillygon rhombus-42 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{1}{\phi^{2}} \right )} + \pi $ ≈ 138.1897°
  • α2 : $ 2 \arctan{\left (\frac{1}{\phi^{2}} \right )} $ ≈ 41.8103°
  • α3 : $ - 2 \arctan{\left (\frac{1}{\phi^{2}} \right )} + \pi $ ≈ 138.1897°
  • α4 : $ 2 \arctan{\left (\frac{1}{\phi^{2}} \right )} $ ≈ 41.8103°

Further Properties

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

  • d1 : $ \frac{2}{\sqrt{1 + \phi^{4}}} $ ≈ 0.714
  • d2 : $ \frac{2 \phi^{2}}{\sqrt{1 + \phi^{4}}} $ ≈ 1.868
and diagonal ratio:
  • d1 / d2 : $ \frac{1}{\phi^{2}} $ ≈ 0.382

Dihedral angles:

  • Minimal concave angle: 75.0000°
  • Minimal convex angle: 75.0000°

Reversed edges: None

Similar Shapes

Model Files

Available gap values:

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