Last Update 12/ 01/ 2005
in Esperanto/ in English/ in Portuguese
You are invited to click in the figure either at first on a Miller indices button and then on the matching button with the three letters, either in the reverse sequence. If a smiling face is issued it means the correct Miller indices for that respective tetrahedron face plane marked with the same letters on the distorted perspective figure was selected, according to the given orientation. The Cartesian axes with origin at o are presented in white and the positive side is indicated by x, y and z. Each Cartesian axis intersects two orthogonal tetrahedron edges, as showed on table 1 with equal colors.
Table 1. Intersection of Cartesian axes and tetrahedron edges.
| Point | Midpoint of edge |
| t | AB |
| u | DC |
| r | AD |
| s | BC |
| v | AC |
| w | DB |
Only the 18 first wrong matches of Miller indices and plane are scored by unhappy faces. The standard time is displayed after the game is done, when the complete set of 4 planes was correctly indexed.
Exercises
1) Are there any parallel or perpendicular face planes in the tetrahedron?
2) Write the Miller indices of all the tetrahedron face planes related by a 4 fold inversion axis.
3) Define the location of a 3 fold axis on a tetrahedron and write the Miller indices of the 3 face planes related by its operation.
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Table of subjects.