Compound of six tetrahedra with rotational freedom
# Compound of six tetrahedra with rotational freedom

Compound of six tetrahedra with rotational freedom :

| Type | Uniform compound |
| - | - |
| Index | $UC_1$ |
| Polyhedra | 6 tetrahedra |
| Faces | 24 triangles |
| Edges | 36 |
| Vertices | 24 |
| Symmetry group | tetrahedral $(T_d)$ |
| Subgroup restricting to one constituent | 4-fold improper rotation $(S_4)$ |

The compound of six tetrahedra with rotational freedom is a uniform polyhedron compound made of a symmetric arrangement of 6 tetrahedra, considered as antiprisms. It can be constructed by superimposing six tetrahedra within a cube, and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces. Each tetrahedron is rotated by an equal (and opposite, within a pair) angle θ. Equivalently, a tetrahedron may be inscribed within each cube in the compound of six cubes with rotational freedom, in such a way as to preserve tetrahedral symmetry.

When θ = 0, all six tetrahedra coincide. When θ is 45 degrees, the more symmetric compound of six tetrahedra (without rotational freedom) arises.

## Gallery

* Compounds of six tetrahedra with rotational freedom
* File:Tetrahedron.stlθ = 0°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(5°).stlθ = 5°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(10°).stlθ = 10°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(15°).stlθ = 15°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(20°).stlθ = 20°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(25°).stlθ = 25°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(30°).stlθ = 30°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(35°).stlθ = 35°
* File:Compound_of_six_tetrahedra_with_rotational_freedom_(40°).stlθ = 40°
* File:Compound_of_six_tetrahedra.stlθ = 45°
