A199549 - OEIS

%I #21 Nov 05 2025 15:22:21

%S 576,576,1152,1440,1440,2880,2880,2880,2880,7200,13824,34560,34560,

%T 34560,34560,69120,69120,86400,172800,172800,829440,829440,2073600,

%U 2073600,4147200,49766400

%N Sorted number of sizes of the automorphism groups of distinct solutions in the mix of regular convex polyhedra.

%C Sorted column 4 of Table 1 in the Cunningham reference.

%H Gabe Cunningham, <a href="https://arxiv.org/abs/1111.1312">Mixing Convex Polytopes</a>, arXiv:1111.1312v1 [math.CO], Nov 5, 2011.

%F a(n) = 4 * A199546(n). - _Andrei Zabolotskii_, Oct 24 2025

%e a(1) = 576 because the mix of the tetrahedron {3, 3} and the octahedron {3,4} has 24 vertices, 144 edges, 96 facets, and the size of the automorphism group (which is also the number of flags) is 576.

%Y Cf. A053016, A199545, A199546.

%K nonn,fini,full

%O 1,1

%A _Jonathan Vos Post_, Nov 07 2011

%E Ordering corrected by _Andrei Zabolotskii_, Oct 23 2025