Last Update 11/ 09/ 2002
in English/ in Esperanto/ in French/ in Portuguese
The figure shows a set of octahedron edges represented mainly in a dark colour in perspective projection with convenient distortion, constituting an instructive application game of elements of symmetry. It works by clicking in the right sequence, the buttons with the respective element of symmetry in such orientation to turn the colour of the edges blue.
The application presents randomly a blue edge as starting point. Seven buttons have the centre of inversion, 3 planes of symmetry and 3 axis of rotation oriented as shown in Table 1.
Table 1. The seven buttons of the interactive picture.
| Button | I | m | m | m | 4 | 3 | 2 |
| Orientation | at origin | contains
x and z |
contains
x and y |
contains z,
bisects x and -y |
coincident
with z |
perpendicular
a (1 -1 1) |
intersection
of m and m |
In Table 1, symbol I means centre of symmetry, m (any colour) indicates reflection plane and 4, 3 and 2 are quaternary, tertiary and binary rotation axes respectively. A scheme with the orientation of the axes cited in table 1 is shown in white colour by clicking on the gray background at the extreme right of the figure on the application, after the columns of buttons. The negative sign in the Miller indices on the penultimate column of table 1 does not obey the conventional form due to a limitation of the language.
Each symmetry operation acts over all blue edges present at the time.
Answer with this game or with the aid of a three-dimensional model:
1) What is the minimum number of clicks on the buttons to solve the task?
2) The buttons that solved the task are always the same?
3) Commuting the symmetry operations gives always the same results?
The time spent can be checked at the end of the game, when the application shows the initial date (related to GMT) at the top of the figure and the final date at the bottom.
To start another game, click in the octahedron.
Please send your comments.
Table of subjects.