Disdyakis triacontahedron

Fillygon disdyakis-triacontahedron normal

Basic Geometry

The 3 edge lengths are:
  • e1 : $ \frac{22 \sqrt{- \sqrt{5} + 5}}{5 \sqrt{- 31 \sqrt{5} + 85}} $ ≈ 1.847
  • e2 : $ \frac{3 \sqrt{19 \sqrt{5} + 65}}{5 \sqrt{- 31 \sqrt{5} + 85}} $ ≈ 1.571
  • e3 : $ 1 $ ≈ 1.000
The 3 angles are:
  • α1 : $ \arccos{\left (\frac{5 \sqrt{- 31 \sqrt{5} + 85} \left(- \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + 1 + \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{44 \sqrt{- \sqrt{5} + 5}} \right )} $ ≈ 58.2379°
  • α2 : $ \arccos{\left (\frac{25 \left(- 31 \sqrt{5} + 85\right) \left(-1 + \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{132 \sqrt{- \sqrt{5} + 5} \sqrt{19 \sqrt{5} + 65}} \right )} $ ≈ 32.7703°
  • α3 : $ \arccos{\left (\frac{5 \sqrt{- 31 \sqrt{5} + 85} \left(- \frac{484 \left(- \sqrt{5} + 5\right)}{25 \left(- 31 \sqrt{5} + 85\right)} + 1 + \frac{9 \left(19 \sqrt{5} + 65\right)}{25 \left(- 31 \sqrt{5} + 85\right)}\right)}{6 \sqrt{19 \sqrt{5} + 65}} \right )} $ ≈ 88.9918°

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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