Great_triakis_octahedron Knowpia

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

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

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

Summary

Proportions edit

References edit

External links edit