Perversely, we decided to add yet another Euler angle convention to the EM community (we did have a good reason at the time). However, on the bright side, the EMAN library has routines to convert to other conventions. EMAN uses a Z,X,Z’ convention (Az, Alt, Phi). That is, first there is a rotation about the Z axis, then about X, then about the new Z axis. When viewing projections, the convention is to look along the Z axis, so a 0,0,0 projection will be a ‘top’ view of the particle. The three rotations are given the names azimuth, altitude and phi. In projection, phi represents rotation in the plane of the projection. For example, Alt=90 will produce a ‘side’ view of the particle, and azimuth will rotate through the various possible side views. The C++/Python 'Euler' object contains code for converting between various EM Euler angle conventions. See libEM/Euler.C for rotation matrices, etc.
| Cn |
Single n-fold rotational axis (n components) |
| Dn |
Single n-fold rotational axis + n 2-fold
rotational
axes 90 degrees from the n-fold, eg - GroEL is approximately D7 (2n
components) |
| tet |
Tetrahedral, also called cubic: 3,2 symmetry,
parent symmetry for octahedral and icosahedral
symmetries, perversely, this is not the full symmetry of a cube. This
symmetry
is supported in EMAN 1.8, but not thoroughly tested. |
| oct |
Octahedral symmetry: 4,3,2. This is the symmetry
of
a cube. (24 components) |
| icos |
Icosahedral symmetry: 5,3,2. (60 components) |
The EMAN convention is for the axis with the highest symmetry to be aligned along Z. So, for a D8 symmetry, the 8-fold axis lies along Z, and the asymmetric triangle spans alt=[0,90] and az=[0,45]. For icosahedral symmetry, the 5-fold lies along Z. Note that this differs from the MRC convention in which 2-folds are aligned with x, y and z.