Great triakis octahedron

Template:Short description Template:Uniform polyhedra db File:Great triakis octahedron.stl In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U₁₉). It has 24 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models.

Proportions

The triangles have one angle of $\arccos (\frac{1}{4}+\frac{1}{2}\sqrt{2})\approx 16.84211623630^{\circ }$ and two of $\arccos (\frac{1}{2}-\frac{1}{4}\sqrt{2})\approx 81.57894188185^{\circ }$. The dihedral angle equals $\arccos (\frac{-3+8\sqrt{2}}{17})\approx 60.72238680964^{\circ }$.

References

• Template:Citation

External links

• Mathworld - Great Triakis Octahedron
• Mathworld - Small Triakis Octahedron
• Uniform polyhedra and duals