Last Update 11/ 09/ 2002
in English/ in Esperanto/ in French/ in Portuguese
The figure shows a set of icosahedron 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 at the right side of the figure may be used to operate the centre of inversion, 2 planes of symmetry and 4 axis of rotation oriented as shown in Table 1.
Table 1. The seven buttons of the interactive picture.
| Buttons | I | m | m | 2 | 2 | 3 | 3 |
| Orientation | at origin | contains
3 |
contains
2 |
contains
(139; 116) (178; 184) |
contains
(84; 90) (232; 210) |
contains
(76; 88) (240; 214) |
contains
(158; 150) |
In Table 1, symbol I means centre of symmetry, m (any colour) indicates reflection plane, 3 and 2 are three fold and binary rotation axes respectively. In the same table axis 3 is perpendicular to the screen.
A scheme with the orientation of axes and planes cited in table 1 is shown by clicking on the gray background at the right side of the figure. Symmetry elements coloured white in the scheme are coloured black in the buttons. Reflection planes are represented by hexagons.
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?
Try to obtain:
1) One or more triangles with blue edges.
2) Independent cycles of 4, 5, 6, 10 or 12 blue edges.
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 icosahedron.
Please send your comments.
Table of subjects.