Complexification of Tetrahedron and Pseudo-Projective Transformations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 1-7
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It is proved that octahedron is the complex version of tetrahedron in the following sense. The symmetry group of tetrahedron, $A_3$, can be regarded as the group of projective transformations of the space $\mathbb{R}\mathbb{P}^2$ that preserve a quadruple of points. This group can be extended to the group of transformations of the space $\mathbb{РЎ}\mathbb{P}^2$ that preserve a quadruple of points and take complex lines into complex ones. This group turns out to be the symmetry group $B_3$ of octahedron.
@article{FAA_2001_35_4_a0,
author = {V. I. Arnol'd},
title = {Complexification of {Tetrahedron} and {Pseudo-Projective} {Transformations}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {1--7},
year = {2001},
volume = {35},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a0/}
}
V. I. Arnol'd. Complexification of Tetrahedron and Pseudo-Projective Transformations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 1-7. http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a0/
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