Interactive examples of Anti-Self-Polar polyhedra

The table below contains examples on the two-dimensional sphere computed by Qingsong Wang in collaboration with Mikhail Katz and Facundo Mémoli . For more discussion and theoretical properties of ASPs, see the arXiv preprint "Extremal spherical polytopes and Borsuk's conjecture"

The computational results on the three-dimensional sphere can be found through this link

Name n: Number of points (Spherical) Diameter f: Max vertices in a facet r: Facets with max vertices t: Triangles in diameter graph Symmetry group Shape
B2 7 2.076537 4 3 4 Z 3 \mathbb{Z}_3 
B3 10 2.093032 4 6 4 Z 3 \mathbb{Z}_3 
B4 13 2.094297 4 9 4 S 3 S_3 
C1 8 2.087071 5 1 4 Z 2 \mathbb{Z}_2 
C2 9 2.093346 5 1 3 Z 2 \mathbb{Z}_2 
C3 9 2.090792 5 1 4 Z 2 \mathbb{Z}_2 
C4 9 2.090160 6 1 5 Z 2 \mathbb{Z}_2 
C5 10 2.093172 5 1 4 Z 2 \mathbb{Z}_2 
C6 10 2.093556 5 2 4 Z 2 \mathbb{Z}_2 
C7 10 2.092404 5 3 4 Z 2 \mathbb{Z}_2 
C8 10 2.091741 7 1 6 Z 2 \mathbb{Z}_2 
D1 10 2.094094 5 1 3 {e}
D2 10 2.093599 6 1 4 {e}
E1 11 2.366612 5 1 0 D 5 D_5