Last Update 11/ 09/ 2002
in English/ in Esperanto/ in French/ in Portuguese
The figure shows a set of tetrahedron 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 from top to bottom to operate the 3-fold axis, 3 planes of symmetry and four-fold inversion axis. The sixth button (with label "C") presents the circumscribed cube. The last button labed "O" presents the inscribed octahedron. The 3-fold axis is the intersection of plane m and m. Plane mcontains the four-fold inversion axis.
A scheme with the orientation of all axes and symmetry planes 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 on the buttons. The other colours are equal in the buttons and in the scheme. Symmetry planes are represented by triangles.
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) A cycle of 4 blue edges.
2) A blue triangle.
3) Two other solutions for item 2.
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 tetrahedron.
Please send your comments.
Table of subjects.