Great triakis octahedron

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.

Great triakis octahedron
Type	Star polyhedron
Face
Elements	F = 24, E = 36 V = 14 (χ = 2)
Symmetry group	Oh, [4,3], *432
Index references	DU19
dual polyhedron	Stellated truncated hexahedron

3D model of a great triakis octahedron

Proportions

The triangles have one angle of ${\displaystyle \arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }}$ and two of ${\displaystyle \arccos({\frac {1}{2}}-{\frac {1}{4}}{\sqrt {2}})\approx 81.578\,941\,881\,85^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-3+8{\sqrt {2}}}{17}})\approx 60.722\,386\,809\,64^{\circ }}$.

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

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