by **wendy** » Sat Feb 22, 2014 7:23 am

The whole point behind the stott-matrix is to allow one to access vector-dots without having to convert to an orthogonal system. It's not really intended for generating vertex coordinates.

Coordinate functions like EPACS and APACS and EP+C and EPEC represent the four subgroups of the cubic symmetry.

APACS is the full octahedral group. EPACS is the pyratohedral, APECS is the tetrahedral group, EP&CS is the octahedral rotational group (eg snub cube), and EPECS is the tetrahedral rotation group. Stating a point is (1,0,0) EPACS means that it is in one of 24 reflection-rotary cells of the pyritohedral group. You might use this information to reduce it to (1,0,0), (0,1,0), (0,0,1) ACS, which is the ordinary rectangular group.

Well, you have AI and EI, all icosahedral and even-icosahedral (snub dodecahedron). These reduce to 5 points in EPACS and EPECS. A point off a mirror (ie has no 0 in the coordinate), would reduce to 5 points to EP, and then to 15 points for ECS or ACS to expand to 60 or 120 points.

The dynkin matrix, applied at the AI point, allows one to find the coordinates of the vertex in different mirrors. A point (a,b,c) reflected in the rectangular mirror A would give (-a,b,c), ie (a, b, c)-a(2,0,0). Here, the icosahedral coordinate of a point reflected in mirror A is (a,b,c)-a(2,-f,0).