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Home > 2009 Mathematical Art Exhibition
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"Five Left Tetrahedral Cosets," by Francisco Lara-Dammer, Indiana University, Bloomington (2008)

Digital print, 20" x 20". "This is a Klein diagram (named after the nineteenth-century German mathematician Felix Klein) that represents A5, the group of symmetries of the icosahedron. Another way of describing A5 is as the alternating group on five elements, namely, the group of all even permutations of five entities. This diagram emphasizes A5's tetrahedral subgroup A4 (the group of symmetries of the tetrahedron, also the group of even permutations of four entities), which has twelve elements, plus the four left cosets of A4. The general diagram is obtained by centrally projecting an icosahedron onto a sphere (with the center of one face projected onto the north pole) and then making a stereographic projection of the sphere down onto a horizontal plane. Each coset has been identified with one color. The circle contains a hundred and twenty regions from which sixty correspond to the dark blue background, and the other sixty are split with the five left cosets. The reason I have realized Klein diagrams is to understand more clearly the beauty of Group Theory." --- Francisco Lara-Dammer, Research assistant. Center for Research on Concepts and Cognition, Indiana University, Bloomington, IN

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American Mathematical Society