Trisha Shetty

A6 polytope

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A6 polytope

In 6-dimensional geometry, there are 35 uniform polytopes with A6 symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A6 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 35 polytopes can be made in the A6, A5, A4, A3, A2 Coxeter planes. Ak graphs have [k+1] symmetry. For even k and symmetric ringed diagrams, symmetry doubles to [2(k+1)].

These 63 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

References

A6 polytope Wikipedia


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