Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (4,4,4,4)

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)(10,19)(11,20)(12,18)(14,17)(15,21)(16,24)(22,26)(23,30)(25,28)(27,32)(29,31);

r1 := (1,3)(2,6)(5,13)(7,17)(8,9)(11,22)(15,19)(16,26)(18,28)(20,29)(24,31)(27,30);

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

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 16 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves