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

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[edit]

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

## References[edit]

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

## External links[edit]

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

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