Pentagonal hexecontahedron

Fillygon pentagonal-hexecontahedron normal

Basic Geometry

The 5 edge lengths are:
  • e1 : $ 1 $ ≈ 1.000
  • e2 : $ 1 $ ≈ 1.000
  • e3 : $ 1 $ ≈ 1.000
  • e4 : $ \frac{\frac{1}{3} + \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{6} + \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{6}}{- 4 \left(- \frac{1}{3} + \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12}\right)^{2} + 2} $ ≈ 1.750
  • e5 : $ \frac{\frac{1}{3} + \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{6} + \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{6}}{- 4 \left(- \frac{1}{3} + \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12}\right)^{2} + 2} $ ≈ 1.750
The 5 angles are:
  • α1 : $ \arccos{\left (- \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12} - \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{1}{3} \right )} $ ≈ 118.1366°
  • α2 : $ \arccos{\left (- \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12} - \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{1}{3} \right )} $ ≈ 118.1366°
  • α3 : $ \arccos{\left (- \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12} - \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{1}{3} \right )} $ ≈ 118.1366°
  • α4 : $ \arccos{\left (- \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12} - \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{1}{3} \right )} $ ≈ 118.1366°
  • α5 : $ \arccos{\left (- 2 \left(- 2 \left(- \frac{1}{3} + \frac{\sqrt[3]{12 \phi \left(- \sqrt{-15 + 81 \phi} + 9\right) + 44}}{12} + \frac{\sqrt[3]{44 + 12 \phi \left(9 + \sqrt{-15 + 81 \phi}\right)}}{12}\right)^{2} + 1\right)^{2} + 1 \right )} $ ≈ 67.4535°

Further Properties

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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