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

Small Group ID = [256,25886], hypertope number 1.

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

r1 := (1,3)(2,6)(5,13)(7,16)(8,9)(11,20)(14,17)(15,24)(18,26)(22,28)(23,25)(30,31);

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

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

• 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, (r0*r2)^2, (r0*r3)^2, (r0*r1)^4, (r1*r2)^4, (r1*r2*r1*r0)^2, (r3*r1*r0*r1)^2, (r1*r3)^4, r2*(r1*r2*r3)^3*r1*r3 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 32 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves