This is figure five of the isogonal hexagons discussion. It shows all twelve rotations and reflections of a typical iso_hex. One of the transformations is the identity. Some digits are underscored to make the pattern clearer.

figure five all have a census of 32
⟨ 6, 0, 3, 4, 2, 1 ⟩			⟨ 6, 1, 2, 4, 3, 0 ⟩
⟨ 0, 3, 4, 2, 1, 6 ⟩			⟨ 0, 6, 1, 2, 4, 3 ⟩
⟨ 3, 4, 2, 1, 6, 0 ⟩			⟨ 3, 0, 6, 1, 2, 4 ⟩
⟨ 4, 2, 1, 6, 0, 3 ⟩			⟨ 4, 3, 0, 6, 1, 2 ⟩
⟨ 2, 1, 6, 0, 3, 4 ⟩			⟨ 2, 4, 3, 0, 6, 1 ⟩
⟨ 1, 6, 0, 3, 4, 2 ⟩			⟨ 1, 2, 4, 3, 0, 6 ⟩