Rank 4 Star diagram with parameters (a,b,c) = (4,8,4)

Small Group ID = [256,25876], 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 := (1,2)(3,5)(4,6)(7,9)(8,12)(10,15)(11,17)(13,20)(14,22)(16,21)(18,25)(19,24)(23,27)(26,29)(28,30)(31,32);

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

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

r3 := (1,5)(2,3)(4,9)(6,7)(8,10)(11,14)(12,15)(13,16)(17,22)(18,23)(19,29)(20,21)(24,26)(25,27)(28,32)(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, (r3*r0)^2, (r3*r1)^4, (r2*r1*r3*r1)^2, (r1*r0*r1*r3)^2, (r2*r1)^2*r2*r0*r1*r2*r1*r0, (r3*r0*r1)^4 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 32 elements

type 2: 8 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 8

• This hypertope does not have non-degenerate leaves