Disdyakis dodecahedron

Fillygon disdyakis-dodecahedron normal

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

Similar Shapes

Model Files

Available gap values:

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