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

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

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

r2 := (3,6)(4,9)(5,12)(7,15)(8,18)(10,21)(13,24)(14,20)(16,22)(19,28)(23,27)(25,29);

r3 := (3,7)(4,10)(5,13)(6,15)(8,19)(9,21)(12,24)(14,20)(18,28)(23,27)(26,30)(31,32);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• 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