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

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References

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

External links

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