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

Small Group ID = [256,25886], hypertope number 3.

• 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 := (1,2)(3,7)(4,6)(5,10)(8,14)(11,18)(13,17)(15,23)(19,22)(21,25)(24,29)(26,28);

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

r2 := (1,4)(2,6)(3,8)(5,11)(7,14)(9,16)(10,18)(12,20)(13,21)(15,24)(17,25)(19,26)(22,28)(23,29)(27,31)(30,32);

r3 := (3,5)(7,10)(8,11)(9,12)(14,18)(16,20)(27,30)(31,32);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 8 elements

type 1: 32 elements

type 2: 8 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves