Visual examples of a theorem of the axonometry
Izidor Hafner
Faculty of Electrical Engineering, University of Ljubljana
Trzaska 25, 1000 Ljubljana, Slovenia
e-mail: izidor.hafner@fe.uni-lj.si
One way to faciliate learning of stereometry is to give
3D illustration instead of usual 2D figures. Here ia an example from the axonometry.
For three angles with the sum Pi there exists a rectangular parallelepiped R with
diagonals AG, CE, DF, BH such that the dihedral angles at the edge AG of the six pairwise symmetric tetrahedra
into which R is decomposed by the planes AGB, AGC, AGD are these angles [1, pg. 136, 2, pg. 249].
Use the following nets to make models.
References
[1] V. G. Boltjanskii, Tretja problema Hilberta, Nauka, Moskva 1977.
[2] B. Jessen, The Algeba of Polyhedra and the Dehn-Sydler Theorem, Mathematica Scandinavica,22 (1968) 241-256.
[3] Martin Kraus' Live3D applet http://www.vis.uni-stuttgart.de/~kraus/index.html.
