1. Mehmet Koca Department of Physics College of Science Sultan Qaboos University Muscat-OMAN kocam@squ.edu.om Bangalore conference, 16-22 December, 2012 1 Rank-4 Coxeter Groups with Quaternions and 4D polytopes

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3. 2.1. Representations of the group elements of rank-4 Coxeter groups with quaternions Correspondence between the rank-4 Coxeter-Weyl groups and the finite subgroups of quaternions Five rank-4 Coxeter groups are described with the quaternionic roots and the quaternionic group elements Bangalore conference, 16-22 December, 2012 3

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5. The Coxeter Dynkin diagram of A 4 Bangalore conference, 16-22 December, 2012 5

6. The F 4 diagram with quaternionic reflection generators Bangalore conference, 16-22 December, 2012 6

7. The F 4 diagram with quaternionic reflection generators Bangalore conference, 16-22 December, 2012 7

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10. 2.2. 4D polytopes with the W(A 4 ) symmetry Bangalore conference, 16-22 December, 2012 10

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13. Duals of the A 4 polytopes Bangalore conference, 16-22 December, 2012 13

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29. 2.5. 4D polytopes with the H 4 symmetry Bangalore conference, 16-22 December, 2012 29

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62. Some polyhedra from the projection of the grand antiprism into 3D space: Bangalore conference, 16-22 December, 2012 62