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

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

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

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

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

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

• 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