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

Small Group ID = [256,25886], hypertope number 2.

• Structure of Group

(C2 x C2 x ((C2 x C2 x C2) : (C2 x C2))) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,9)(6,10)(12,18)(13,19)(21,26)(22,27)(28,31);

r1 := (1,2)(3,7)(4,8)(5,11)(6,13)(9,17)(10,19)(12,21)(14,20)(15,22)(16,24)(18,26)(23,28)(25,29)(27,30)(31,32);

r2 := (2,5)(4,9)(6,12)(7,14)(10,18)(15,23)(24,29)(30,32);

r3 := (1,3)(2,6)(4,10)(5,12)(7,15)(8,16)(9,18)(11,20)(13,22)(14,23)(17,25)(19,27)(21,28)(24,30)(26,31)(29,32);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r2^2, r1^2, r3^2, (r3*r2)^2, (r3*r0)^2, (r0*r2)^2, (r1*r3)^4, (r1*r3*r1*r2)^2, (r1*r2)^4, (r1*r0*r1*r2)^2, (r1*r0)^4, r3*(r1*r3*r0)^3*r1*r0 ];;

• Number of Elements of each type

type 0: 8 elements

type 1: 32 elements

type 2: 4 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves