Rank 4 Star diagram with parameters (a,b,c) = (4,4,6)

Small Group ID = [192,1472], hypertope number 1.

• Structure of Group

S4 x D8

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(7,9);

r1 := (1,2)(4,8)(6,10)(7,11)(9,12);

r2 := (1,3)(2,5)(4,7)(6,9)(8,12)(10,11);

r3 := (1,4)(2,6)(3,7)(5,9);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;

G := F/[ r3^2, r1^2, r2^2, r0^2, (r2*r3)^2, (r2*r0)^2, (r0*r3)^2, (r0*r2*r1)^4, r1*r0*(r2*r1)^2*r3*r0*r2*r3*r1*r2, (r0*(r1*r3)^2*r1)^2, (r1*r3)^6, r2*r1*r0*r2*(r3*r1)^2*r2*r1*r2*r0*(r3*r1)^2*r0, (r3*r2*r1*r3*r2*r0*r1*r3*r1)^2 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 24 elements

type 2: 4 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves