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

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