**PURPOSE**- Creates a document file containing symmetry Euler angles. Creates
angles for following symmetry groups:

(C)yclic group, with only one axis of rotational symetry

(CI)Cyclic group w/ inversion, or dihedral groups

(T)etrahedral group, where ref. structure is 4-sided polygon

(O)ctohedral group, that is also holohedral, effectively a cube

(I)cosahedral group, regular 20-sided closed polygon.

(G)roel, 7 fold rotational with inversion.

**SEE ALSO****RT 3**[RoTate - volume, slow] **RT SQ**[Rotate and Shift - image, Quadratic interpolation ||] **AP SH**[Alignment - multi-reference, exhaustive rotation & shift ||*] **AP REF**[Alignment - multi-reference, rotation & shift ||*]

**USAGE**- .OPERATION: SY

- .SYMMETRY DOCUMENT FILE: DOC002

[Enter name of output document file.].SYMMETRY TYPE (C/CI/T/O/I/G): C

[Enter symmetry type.] - If the symmetry type was 'C' or 'CI' the following question will appear.
- .SYMMETRY FOLDNESS: 5

[Enter rotational symmetry parameter.]

**NOTES**

- Assumes right-handed coordinate system, and rotations as
described for SPIDER's
Euler angles.

- Objects with rotational symmetry (types: 'C' and Ci') should
be oriented with rotational axis parallel with the Z axis and
centered within the volume.
- Objects with tetrahedral symmetry should be oriented with
the 3-fold rotational axis parallel with the Z axis,
with a vertex on the positive Z axis. Also, a vertex should be
along the positive X axis.

- Objects with icosahedral symmetry should be oriented with
The he axis of 5-fold rotational symmetry along the Z
axis. When the structure is viewed from the positve Z axis, one
edge should point along the positive X axis.
- Objects with Octo/holo-hedral(cubic) symmetry should be oriented with
so that each axis is normal to a face of the cube.

- Useful discussions of the use of Euler angles to rotate 3D bodies can
be found at mathworld and
here.
Please note that these websites do not necessarily use the same
conventions as SPIDER does, but
this
does.
- Implemented by: Jamie Lebarron.

**SUBROUTINES**- SYMANG

**CALLER**- DRIV3

© Copyright Notice / Enquiries: spider@wadsworth.org