The normal operating mode, called SHAPE mode, is restricted to the symmetry of the 32 crystallographic point groups. The QSHAPE mode avoids this restriction by using Cartesian reference axes and Cartesian symmetry matrices. The choice is made in the Modes menu.
Solids which show external morphology, X-ray and/or electron diffraction patterns of apparent symmetry not belonging to one of the 32 crystal classes have been termed quasi-crystals; hence the name Quasi-SHAPE or QSHAPE. Crystals cannot have symmetry axes of order five, or higher than six, so that quasi-crystals cannot truly have this symmetry (or else they cannot be true crystals). Nevertheless their external form often shows apparent icosahedral or other non-crystallographic symmetry. Polyhedra with non-crystallographic symmetry are also of interest from a purely geometric standpoint; the icosahedron and pentagonal dodecadron are among the five Platonic solids.
Since reference axes based on lattice translations are not applicable to quasi-crystals (this term will be used here for all solids with faces like crystals, but which have non-crystallographic symmetry), the QSHAPE mode always uses a Cartesian axis system. Whereas the SHAPE operating mode, in order to find all the symmetry equivalents of a face, uses a simplified system of transformation of the indices in integral form, the QSHAPE mode must multiply the indices by Cartesian symmetry matrices, one for each symmetry operation in the point group. The sets of symmetry matrices are in separate files, which must be generated beforehand with the auxiliary program SYMGRP, described in the next section. The symmetry files for the pentagonal and icosahedral groups have already been generated and are provided on the SHAPE disk(s).
In calculating the locations of corners, the SHAPE mode makes use of sectors defined by mirror planes (see I-3). Since the orientations of mirror planes cannot be fixed beforehand in the general case of non-crystallographic symmetry, this method cannot be used in the QSHAPE mode, and calculations may be much slower. Because of the necessity of generating the symmetry files beforehand, and the usually slower execution for crystals with mirror planes, the QSHAPE mode is not recommended for use with true crystals, although it is perfectly capable of drawing any crystal.
Operation in the QSHAPE mode differs from that in the SHAPE mode in only a few respects: otherwise, everything in the instructions pertains to both modes.
1) In entering a crystal using the Title/Axes and Symmetry dialogs (Input1 menu) you do not supply the axis lengths and angles and crystal class. Rather, the axes are always Cartesian and in the Symmetry dialog you must give the name of a file containing the symmetry matrices. Normally such a file will have been generated by the auxiliary program SYMGRP (next section), and will have the extension .SYM.
2) The indices for forms, faces and vectors are decimals, rather than integers (whole numbers). You do not need to enter a decimal point, and you can enter integral indices of any size, but once entered the indices will be normalized to a length of one (h2 + k2 + l2 = 1.0). QSHAPE uses a threshold value of 0.0001 to test whether numbers are the same; thus five significant figures are usually sufficient.
3) Because of the necessity of storing all the symmetry matrices, the number of epitaxial crystals allowed in the QSHAPE mode is smaller than that in the SHAPE mode: see the README file for current limits.
4) If you are in normal mode and you read a data file written with QSHAPE mode, you will be switched automatically (with your approval) to the QSHAPE mode, and vice versa. However, files written by V4.1 or earlier SHAPE for DOS must be converted to the current format with the DOS program FILEUP.